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Classroom Tips and Techniques: Stepwise Solutions in Maple - Part 2 - Linear Algebra Robert J. Lopez Emeritus Professor of Mathematics and Maple Fellow MaplesoftJSFH JSFH

JSFH In the preceding article Stepwise Solutions in Maple - Part 1, we detailed the Maple tools for obtaining stepwise solutions of problems in algebra, and calculus of one and several variables. In this sequel, we detail the stepwise tools available in linear algebra. Stepwise solutions in vector calculus will be discussed in our next article. These tools include tutors that implement Gaussian arithmetic for solving linear systems and inverting a square matrix, calculation of eigenvalues and eigenvectors, and task templates that provide simplified interfaces to some of the visualizations tools in the Student LinearAlgebra package. There is also a task template for visualizing the transforming action of a matrix in the plane. But again, we point out that Maple "does" symbolic math, and can therefore be directed to implement the steps of nearly any algorithmic computation.

JSFH Gaussian elimination combines elementary row operations to transform a matrix into a row-equivalent upper triangular matrix. Table 1 illustrates the stepwise tool for this, the Gaussian Elimination tutor. 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Table 1 Gaussian Elimination tutor applied to an augmented matrix JSFH If row-reduction were being implemented by hand, the first step would most likely be the addition of row 3 to row 1, thereby creating a 1 in the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRidGMEY0RjRGNA==-position. This was done to start the reduction, and the remaining steps shown in Table 1 are the result of the "All Steps" button. If the "Next Step" button were used to step through the reduction, annotation for each step would appear in the upper right-hand window of the tutor. Since the matrix in Table 1 is augmented, it arose from a linear system LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2J1EiYkYnRjhGOkY8Rj5GRA==. To continue with the solution process, press the "Solve System" button, to obtain the contents of Table 2 where back-substitution is then applied stepwise. 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Table 2 Back-substitution completes the calculation started in Table 1 JSFH Pressing the "Equations" button writes the equations corresponding to the upper triangular matrix in Table 1. In succession, pressing the "Solve" buttons implements back-substitution. JSFH

JSFH Using the same elementary row operations as the Gaussian Elimination tutor, the Gauss-Jordan Elimination tutor illustrated in Table 3 row-reduces the augmented matrix in Table 1 to reduced row-echelon form. JSFHJSFH 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Table 3 Reduced row-echelon form by elementary row operations JSFH

JSFH The Linear System Solving tutor is simply a portal to either the Gaussian Elimination tutor or the Gauss-Jordan Elimination tutor. The doorway is shown in Table 4. JSFH 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Table 4 The Linear System Solving tutor JSFH

JSFH The inverse of the square matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= can be found by solving for its columns LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiY0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1GLzYlUSJrRicvRjZGNC9GOVEnaXRhbGljRidGQkZDLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjlRJ25vcm1hbEYn via the equations 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, where the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EiZUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1GLzYlUSJrRicvRjZGNC9GOVEnaXRhbGljRidGQkZDLyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjlRJ25vcm1hbEYn are the columns of the identity matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Writing all these systems at once, and solving by transforming to reduced row-echelon form is a standard textbook method for finding the inverse. This calculation is implemented by the Matrix Inverse tutor, as shown in Table 5. Just the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is entered - the tutor augments LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= with the identity. JSFH 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Table 5 Matrix inversion by elementary row operations leading to reduced row-echelon form. JSFH

JSFH The Eigenvalues tutor steps through the calculation of the eigenvalues of a square matrix. The four steps implemented are shown on the left in Table 6, with bold font used to indicate the present step.JSFH JSFH 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Table 6 First panel of the Eigenvalues tutor JSFH The remaining calculations are summarized in Table 7. Calculate 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 Find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEkZGV0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEiQUYnRi9GMi9GM1Enbm9ybWFsRidGPUY9 Solve for roots 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

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 so the eigenvalues are LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjdGJ0Y5LUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRlA2JFEiNUYnRjlGOQ== Table 7 The final three steps in the Eigenvalues tutor JSFH

JSFH The Eigenvectors tutor steps through the calculation of the eigenvectors of a square matrix. Table 8 shows the initial panel for this tutor. 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Table 8 Initial panel for the Eigenvectors tutor If the "Yes" button is selected, the Eigenvalues tutor (see Tables 6 and 7) is launched. If the "No" button is selected, then the panel shown in Table 9 is launched. Note that the default matrix for both the Eigenvalues and Eigenvectors tutors is 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 with eigenvalues LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIyRidGLy1GLDYtUSIsRidGL0YyL0Y2USV0cnVlRidGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFUSwwLjMzMzMzMzNlbUYnLUZHNiRRIjFGJ0YvRkotRkc2JFEiM0YnRi9GLw==. 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Table 9 Computing eigenvectors in the Eigenvectors tutor Selecting a "Find Eigenvector" button leads to the three panels summarized in Table 10. 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 JSFH JSFH Table 10 Stepwise calculation of the eigenvector corresponding to the eigenvalue LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=

Nine of the ten visualization task templates for linear algebra are based on visualization commands in the Student Linear Algebra package. The PlanePlot, ProjectionPlot, and VectorSum commands, implemented in four of these visualization task templates, provide a measure of stepwise calculations. The Matrix Action task template is independent of the Student package, but also provides a significant stepwise presence in the subject.

JSFH Table 11 shows the functioning of the Matrix Action 2-D task template. Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualization\342\211\273Matrix Action 2-D Matrix Action: 2-D Matrix: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUEY+ LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGRA== 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 Eigenpairs 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSUYy LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EidkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUEY+ 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 use DocumentTools,LinearAlgebra in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local A,q1,q2,q3,B,NA,X,X0,AX0,L,T0,Q,q,R,C; Do(A = %MathContainer0): if A=NULL then return;end if; NA := Norm(evalf(A),2); Do(%MathContainer4 = NA); q1,q2 := Eigenvectors(A): Q := [Column(q2,1),Column(q2,2)]; q := evalf(Q); Do(%MathContainer5 = MathML[Export](evalf(q1,4))): q3 := evalf([Normalize(Column(q2,1),2),Normalize(Column(q2,2),2)],4); Do(%MathContainer6 = MathML[Export](q3)): B := ceil(NA); Do(%Plot0 = plot(0,x=-B..B,y=-B..B)): X := plots[display](plots[arrow]([0,0],[1,0],color=black)); X0 := plottools[circle]([0,0],1,color=red); #Do(%Plot1 = plots[display]([X,X0],scaling=constrained, tickmarks=[0,0])): AX0 := A.<1,0>; R := VectorCalculus:-ConvertVector(A.<cos(t),sin(t)>,position); C := VectorCalculus:-PlotPositionVector(R,t=0..2*Pi,curveoptions=[color=red,linestyle=2]); Do(%Plot0 = plots[display]([C,plots[arrow]([0,0],AX0,color=black)],view=[-B..B,-B..B],scaling=constrained)); Do(%MathContainer1 = <1,0>); Do(%MathContainer2 = AX0); Do(%MathContainer3 = evalf(LinearAlgebra:-Norm(AX0,2))); if not has(q,I) then qq := map(Normalize,q,2); v1 := plots[display](plots[arrow]([0,0],qq[1],color=red)); v2 := plots[display](plots[arrow]([0,0],qq[2],color=green)); v3 := plots[display](plots[arrow]([0,0],-qq[1],color=red)); v4 := plots[display](plots[arrow]([0,0],-qq[2],color=green)); Do(%Plot1 = plots[display]([X0,X,v1,v2,v3,v4],scaling=constrained, tickmarks=[0,0])): else Do(%Plot1 = plots[display]([X0,X],scaling=constrained, tickmarks=[0,0])): end if; end module; end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() end module; end use; LSUlUExPVEc2JS0lJVRFWFRHNiQ3JCQiIiEhIiIkIiIhISIiLSUpX1RZUEVTRVRHNiNRR1ZlY3RvcnN+c2hvdWxkfmhhdmV+dGhlfnNhbWV+ZGltZW5zaW9uNiItJSpBWEVTU1RZTEVHNiMlJU5PTkVHLSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIjXSEiIi0lKUJPVU5EU19ZRzYjJCIjXSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSEpPSEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiUhKT0hIiItJSlDSElMRFJFTkc2Ig== use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. Do(%MathContainer0 = NULL); Do(%MathContainer1 = NULL); Do(%MathContainer2 = NULL); Do(%MathContainer3 = NULL); Do(%MathContainer4 = NULL); Do(%MathContainer5 = NULL); Do(%MathContainer6 = NULL); Do(%Plot0 = plots[display](plots[textplot]([0,0,""]),axes=none)); Do(%Plot1 = plots[display](plots[textplot]([0,0,""]),axes=none)); end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGSUY1LUY2Ni1RIj1GJ0YyRjlGO0Y9Rj9GQUZDRkUvRkhRLDAuMjc3Nzc3OGVtRicvRktGUEYyuse DocumentTools,LinearAlgebra in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local s,t,A,Ax,MAx,X0,B,NA,p1,p2,q1,q2,q,qq,Q,R,C,z; t := evalf(Pi/180); Do(s = %Slider0); Do(%Label0(caption) = s); Do(A = %MathContainer0); if A=NULL then return;end if; NA := evalf(LinearAlgebra:-Norm(A,2),10); B := ceil(NA); x := map(evalf,<fnormal(cos(s*t)),fnormal(sin(s*t))>,4); Ax := map(evalf,A.x,4); MAx := evalf(LinearAlgebra:-Norm(Ax,2),10); Do(%MathContainer1 = x); Do(%MathContainer2 = Ax); Do(%MathContainer3 = MAx); Do(%MathContainer4 = NA); R := VectorCalculus:-ConvertVector(A.<cos(z),sin(z)>,position); C := VectorCalculus:-PlotPositionVector(R,z=0..2*Pi,curveoptions=[color=red,linestyle=2]); X0 := plottools[circle]([0,0],1,color=red); p1 := plots[display](plots[arrow]([0,0],Ax,color=black),view=[-B..B,-B..B],scaling=constrained); p2 := plots[display](plots[arrow]([0,0],x,color=black)); Do(%Plot0 = plots[display]([C,p1])); q1,q2 := Eigenvectors(A): Do(%MathContainer5 = MathML[Export](evalf(q1))); Q := [Column(q2,1),Column(q2,2)]; q := evalf(Q); qq := map(Normalize,q,2); Do(%MathContainer6 = MathML[Export](evalf(qq,4))); if not has(q,I) then v1 := plots[display](plots[arrow]([0,0],qq[1],color=red)); v2 := plots[display](plots[arrow]([0,0],qq[2],color=green)); v3 := plots[display](plots[arrow]([0,0],-qq[1],color=red)); v4 := plots[display](plots[arrow]([0,0],-qq[2],color=green)); v5 := plots[display](plottools[arc]([0,0],1/3,0..s*Pi/180),linestyle=2); Do(%Plot1 = plots[display]([X0,p2,v1,v2,v3,v4,v5],scaling=constrained, tickmarks=[0,0])): else Do(%Plot1 = plots[display]([X0,p2],scaling=constrained, tickmarks=[0,0])): end if; end module; end use; = with(Student:-LinearAlgebra): TTdSMApJNVJUQUJMRV9TQVZFLzUyODQ3MTQwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjJSIjIiMmJSJtRzYkIiIiRiomRig2JCIiI0YqJkYoNiRGKkYtJkYoNiRGLUYtRiY= Table 11 Matrix Action 2-D task template JSFH After entering the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, press the Start button, which then populates all the other fields. The slider at the bottom controls the unit vector x that appears in black in the lower graph. As the slider is moved, the varying components of x and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== are displayed. The length of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== is also computed and displayed just above the 2-norm of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. The vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== is plotted in the upper graph where the dotted curve traces the trajectory that the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== would make as the unit vector x traversed the unit circle. The eigenvalues and eigenvectors (normalized) of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= are displayed, and in the lower graph, these unit eigenvectors are graphed, one in red and one in green. Since an eigenvector is actually an invariant direction, the negative of each eigenvector is also plotted. If the slider is adjusted so that the length of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== matches the 2-norm of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the vector LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9L0YzUSdub3JtYWxGJw== in the upper graph should be at its maximum length. JSFH

JSFH The PlanePlot command will draw a plane that is specified by an equation, by a normal vector and a point, and by a pair of (basis) vectors and a point. In addition, there are a number of parameters that control what is added to the plot, such things as the point on the plane nearest to the origin, etc. The Plane Plot task template provides a syntax-free interface for this command, but a number of the parameter settings have necessarily been hard-coded for simplicity. JSFH Table 12 shows the task template used to draw the plane determined by the basis vectors JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

JSFH and the point JSFH 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkobWFjdGlvbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUklbXJvd0dGJDYmLUknbXRhYmxlR0YkNjctSSRtdHJHRiQ2Ji1JJG10ZEdGJDYoLUkjbW5HRiQ2JFEiMkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGQy8lK2dyb3VwYWxpZ25HRkMvJShyb3dzcGFuR1EiMUYnLyUrY29sdW1uc3BhbkdGSkZBRkRGRi1GNTYmLUY4NigtRi82JS1JI21vR0YkNi1RKiZ1bWludXMwO0YnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlkvJSlzdHJldGNoeUdGWS8lKnN5bW1ldHJpY0dGWS8lKGxhcmdlb3BHRlkvJS5tb3ZhYmxlbGltaXRzR0ZZLyUnYWNjZW50R0ZZLyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGYm8tRjs2JEZKRj5GPkZBRkRGRkZIRktGQUZERkYtRjU2Ji1GODYoLUY7NiRRIjRGJ0Y+RkFGREZGRkhGS0ZBRkRGRi8lJmFsaWduR1ElYXhpc0YnL0ZCUSliYXNlbGluZUYnL0ZFUSZyaWdodEYnL0ZHUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdRJXRydWVGJy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRlxxLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmdxLyUmZnJhbWVHRmdxLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGWS8lLWVxdWFsY29sdW1uc0dGWS8lLWRpc3BsYXlzdHlsZUdGWS8lJXNpZGVHRmRwLyUwbWlubGFiZWxzcGFjaW5nR0ZkcS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSlyZWFkb25seUdGWUY+Rj4vSSttc2VtYW50aWNzR0YkUSpDb2xWZWN0b3JGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zecy8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRKjE1MjM4NTc2NEYn

JSFH Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Plane Plot Graph of a Plane Specify a plane in one of the following ways: Equation Normal vector and a point Two vectors in the plane (basis) and a point Obtain plot of plane and Normal vector Equation of the plane Two vectors in the plane The point on the plane closest to the origin The number of digits in the returned data is controlled by the slider. Click the icon below to execute the PlanePlot command. Variables: use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local temp1; Do(temp1 = %MathContainer8); if temp1=NULL then Do(%RadioButton4 = true); Do(%RadioButton1 = false); end if; end module; end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local temp1; Do(temp1 = %MathContainer9); if temp1=NULL then Do(%RadioButton4 = true); Do(%RadioButton2 = false); end if; end module; end use; 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 use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local temp1; Do(temp1 = %MathContainer10); if temp1=NULL then Do(%RadioButton4 = true); Do(%RadioButton3 = false); end if; end module; end use; 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 Digits = use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. Do(%Label1(caption) = %Slider1); end use; = use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. Do(%MathContainer7 = NULL); Do(%MathContainer8 = NULL); Do(%MathContainer9 = NULL); Do(%MathContainer10 = NULL); Do(%Slider1(value) = 4); Do(%Label1(caption) = 4); Do(%TextArea0 = NULL); Do(%RadioButton4 = true); Do(%RadioButton1(value) = false); Do(%RadioButton2(value) = false); Do(%RadioButton3(value) = false); end use; JSFH infolevel[Student[LinearAlgebra]]:=1: use DocumentTools,Student[LinearAlgebra] in proc() local temp1,VAR,p,P,N; Do(%TextArea0 = NULL); Do(temp1 = %MathContainer7); if temp1=NULL then Do(%TextArea0 = "Provide 3 variables");return; elif type([temp1],'list'('list'('name'))) then if nops(indets(temp1))=3 then VAR:=temp1; else Do(%TextArea0 = "Incorrect number of variables");return; end if: elif type([temp1],'list'('name')) then if nops(indets([temp1]))=3 then VAR:=[temp1]; else Do(%TextArea0 = "Incorrect number of variables");return; end if: else Do(%TextArea0 = "Cannot fathom entry for variables");return; end if: if Do(%RadioButton1) then Do(P = %MathContainer8); elif Do(%RadioButton2) then Do(P = %MathContainer9); elif Do(%RadioButton3) then Do(P = %MathContainer10); else Do(%TextArea0 = "Select one form of Plane");return; end if; Do(N = %Slider1); SetDefault(infodigits=N): if type([P],'list'(`=`)) or type([P],'list'(`+`)) then plots[display](PlanePlot(P, VAR, axes = boxed, labels = VAR, showbasis, orientation = [-50, 65], title="",shownearestpoint, nearestpointoptions=[color=black]),axes=box,transparency=.6): else plots[display](PlanePlot(P, axes = boxed, labels = VAR, showbasis, orientation = [-50, 65], planeoptions = [transparency = .8],title="",shownearestpoint, nearestpointoptions=[color=black]),axes=box): end if; end(); end use; infolevel[Student[LinearAlgebra]]:=0: Student[LinearAlgebra][SetDefault](infodigits=4):

normal vector: <.53452, -1.8708, 1.0690> equation of plane: <.53452*x-1.8708*y+1.0690*z = 7.21605353130000005> point on plane nearest origin: <.78261, -2.7391, 1.5652> basis vectors: <1., 2., 3.>, <-2., 0., 1.>

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Table 12 Plane Plot visualization task template JSFH The slider at the bottom of the template controls the number of digits used in reporting most of the data above the graph. The graph itself shows the plane, the normal vector (in orange) drawn at the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, a vector (in black) from the origin to the point on the plane nearest the origin, a vector (in red) from the origin to the point LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, and the basis vectors (in blue). JSFH

JSFH The ProjectionPlot command in the Student Linear Algebra package will project a vector onto a one- or two-dimensional subspace. This dual functionality has been distributed across two different task templates. The task template "Projection Plot onto 1-D" projects a vector onto a one-dimensional subspace. A vector in the plane can be projected onto another vector, or onto a line through the origin. The projection and the orthogonal component are computed; a graph is drawn for vectors that are completely numeric. Table 13 contains an example of the projection of one planar vector onto another. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Projection Plot onto 1-D Projection onto 1-D Subspace Vector to be projected Project onto use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%RadioButton6)=false then Do(%ComboBox0(enabled)=false); Do(%Label2(enabled)=false); Do(%Label3(enabled)=false); end if; end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%RadioButton5)=false then Do(%ComboBox0(enabled)=true); Do(%Label2(enabled)=true); Do(%Label3(enabled)=true); end if; end use; [x\134,y],otheruse DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%ComboBox0)=[x,y] then Do(%MathContainer14=NULL);end if; end use; use DocumentTools, plots, Student[LinearAlgebra] in module() local B,A,X,Y,Z,q1,q2,FIG, temp; Do(B = %MathContainer11): if Do(%RadioButton5) then Do(A = %MathContainer12); if nops([A])=0 then Do(%Plot2 = display(textplot([0,0,"Provide a vector onto which to project"]),axes=none)); else if Dimension(A)<>Dimension(B) then Do(%Plot2 = display(textplot([0,0,"Vectors should have the same dimension"]),axes=none));return; elif nops(select(type,indets(A),name))<>0 or nops(select(type,indets(B),name))<>0 then Do(%Plot2 = display(textplot([0,0,"No graph can be drawn if vectors are not numeric"]),axes=none));return; elif Dimension(A)=2 and Dimension(B)=2 then FIG := ProjectionPlot(B,A, title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black]): elif Dimension(A)=3 and Dimension(B)=3 then FIG := ProjectionPlot(B,A, title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black], axes=box,labels=[x,y,z],orientation=[-55,50]): end if; Do(%Plot2 = FIG): end if; end if; if Do(%RadioButton6) then if Dimension(B)=3 and Do(%ComboBox0)=[x,y] then Do(%Plot2 = display(textplot([0,0,"Variables can't be [x,y] in 3D"]),axes=none));return;end; if Dimension(B)=3 and Do(%ComboBox0)=other then Do(temp = %MathContainer14); if nops([temp])=0 then Do(%MathContainer14 = MathML[Export]("???"));return;end if; X:=temp[1];Y:=temp[2];Z:=temp[3]; Do(A = %MathContainer13); FIG := ProjectionPlot(B,A, [X,Y,Z],title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black], axes=box,labels=[X,Y,Z],orientation=[-55,50]): Do(%Plot2 = FIG); return;end if; if Do(%ComboBox0)=[x,y] then X:=x;Y:=y;end if; if Do(%ComboBox0)=other then Do(temp=%MathContainer14);X:=temp[1];Y:=temp[2];end if; Do(q1 = %MathContainer13); if is(q1=NULL) then Do(%MathContainer16=MathML[Export]("Provide equation of a line thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer15=MathML[Export]("Declared variables must match those in equation of line"));return;end if; if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer16=MathML[Export]("The line does not pass thru origin")); else FIG := ProjectionPlot(B,q2,[X,Y], title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black]); Do(%Plot2 = FIG); end if; end if; end if; end module; end use; use DocumentTools in Do(%MathContainer11 = NULL); Do(%MathContainer16 = NULL); Do(%MathContainer12 = NULL); Do(%MathContainer13 = NULL); Do(%MathContainer15 = NULL); Do(%MathContainer14 = NULL); Do(%Plot2 = plots[display](plots[textplot]([0,0," "]),axes=none)); end use; 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 use DocumentTools, Student[LinearAlgebra] in module() local B,A,BA,q1,q2,X,Y,temp,Temp; Do(B = %MathContainer11): if Do(%RadioButton5) then Do(A = %MathContainer12); if nops([A])=0 then Do(%MathContainer15 = MathML[Export]("Provide a vector onto which to project")); else Temp := GetProperty(MathContainer16,value); if StringTools:-Has(Temp,"P") then Do(%MathContainer16 = NULL);end if; if Dimension(B)=Dimension(A) then BA:=(B.A)/(A.A)*A; Do(%MathContainer15 = BA); else Do(%MathContainer15 = MathML[Export]("Vectors should have the same dimension"));return;end if; end if; end if; if Do(%RadioButton6) then if Dimension(B)=3 and Do(%ComboBox0)=[x,y] then Do(%MathContainer15 = MathML[Export]("Variables can't be [x,y] in 3D"));return;end if; if Dimension(B)=3 and Do(%ComboBox0)=other then Do(A = %MathContainer13); BA := (B.A)/(A.A)*A; Do(%MathContainer15 = BA); return; end if; if Do(%ComboBox0)=[x,y] then X:=x;Y:=y;end if; if Do(%ComboBox0)=other then Do(temp=%MathContainer14);X:=temp[1];Y:=temp[2];end if; Do(q1 = %MathContainer13); if is(q1=NULL) then Do(%MathContainer15=MathML[Export]("Provide equation of a line thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer15=MathML[Export]("Declared coordinates must match variables in equation of line"));return;end if; if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer15=MathML[Export]("The line does not pass thru origin")); else if has(q2,X) and has(q2,Y) then A:=<1,coeff(solve(q2,Y),X)>;BA:=(B.A)/(A.A)*A;Do(%MathContainer15 = BA); elif has(q2,X) and not has(q2,Y) then BA:=<0,B[2]>;Do(%MathContainer15 = BA); else BA:=<B[1],0>;Do(%MathContainer15 = BA); end if; end if; end if; end if; end module; end use; use DocumentTools in module() local temp; try GetProperty(MathContainer15,expression); catch: return; end try; Do(temp = %MathContainer15); if nops([temp])=0 then return;end if; Do(%MathContainer15 = evalf(temp)); end module; end use; use DocumentTools, Student[LinearAlgebra] in module() local A,B,BA,BpA,q1,q2,X,Y,temp; Do(B = %MathContainer11): if Do(%RadioButton5) then Do(A = %MathContainer12); if nops([A])=0 then Do(%MathContainer16 = MathML[Export]("Provide a vector onto which to project")); else temp := GetProperty(MathContainer15,value); if StringTools:-Has(temp,"P") then Do(%MathContainer15 = NULL);end if; if Dimension(B)=Dimension(A) then BA:=(B.A)/(A.A)*A; BpA:=B-BA; Do(%MathContainer16 = BpA); else Do(%MathContainer16 = MathML[Export]("Vectors should have the same dimension"));return;end if; end if; end if; if Do(%RadioButton6) then if Dimension(B)=3 and Do(%ComboBox0)=[x,y] then Do(%MathContainer16 = MathML[Export]("Variables can't be [x,y] in 3D"));return;end if; if Dimension(B)=3 and Do(%ComboBox0)=other then Do(A = %MathContainer13); BA := (B.A)/(A.A)*A; BpA := B-BA; Do(%MathContainer16 = BpA); return; end if; if Do(%ComboBox0)=[x,y] then X:=x;Y:=y;end if; if Do(%ComboBox0)=other then Do(temp=%MathContainer14);X:=temp[1];Y:=temp[2];end if; Do(q1 = %MathContainer13); if is(q1=NULL) then Do(%MathContainer16=MathML[Export]("Provide equation of a line thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y},`subset`)=false then Do(%MathContainer16=MathML[Export]("Declared coordinates must match variables in equation of line"));return;end if; if eval(q2,[X=0,Y=0])<>0 then Do(%MathContainer16=MathML[Export]("The line does not pass thru origin")); else if has(q2,X) and has(q2,Y) then A:=<1,coeff(solve(q2,Y),X)>;BA:=(B.A)/(A.A)*A;BpA:=B-BA;Do(%MathContainer16 = BpA); elif has(q2,X) and not has(q2,Y) then BpA:=<B[1],0>;Do(%MathContainer16 = BpA); else BpA:=<0,B[2]>;Do(%MathContainer16 = BpA); end if; end if; end if; end if; end module; end use; use DocumentTools in module() local temp; try GetProperty(MathContainer16,expression); catch: return; end try; Do(temp = %MathContainer16); if nops([temp])=0 then return;end if; Do(%MathContainer16 = evalf(temp)); end module; end use; with(Student:-LinearAlgebra): with(Student:-LinearAlgebra): Table 13 Projection of one planar vector onto another JSFH

JSFH The ProjectionPlot command in the Student Linear Algebra package will project a vector onto a one- or two-dimensional subspace. This dual functionality has been distributed across two different task templates. The task template "Projection Plot onto 2-D" projects a vector onto a two-dimensional subspace, defined either by its basis, or by the equation of a plane through the origin. The projection and the orthogonal component are computed; a graph is drawn for vectors that are completely numeric. Table 14 contains an example of the projection of a vector onto the plane spanned by a given basis of two other vectors. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Projection Plot onto 2-D Project Vector onto Plane in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2KFEoJiM4NDc3O0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJStmb3JlZ3JvdW5kR1EqWzAsMCwyNTVdRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRj0tRiM2KC1JI21uR0YkNidRIjNGJ0YyRjhGO0Y+RjIvRjZGNEY4L0Y8USxib2xkLWl0YWxpY0YnRj4vJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnL0Y8USdub3JtYWxGJw== Vector to be projected: Project onto plane: use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%RadioButton8)=false then Do(%ComboBox1(enabled)=false); Do(%Label4(enabled)=false); Do(%Label5(enabled)=false); end if; end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%RadioButton7)=false then Do(%ComboBox1(enabled)=true); Do(%Label4(enabled)=true); Do(%Label5(enabled)=true); end if; end use; [x\134,y\134,z],otheruse DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. if Do(%ComboBox1)=[x,y] then Do(%MathContainer20=NULL);end if; end use; use DocumentTools, plots, Student[LinearAlgebra] in module() local a,B,A,X,Y,Z,q1,q2,FIG, temp; Do(B = %MathContainer17): if not type(B,Vector[column]) then Do(%Plot3 = display(textplot([0,0,"Please provide a 3-component column vector to project"]),axes=none));return;end if; if Dimension(B)<>3 then Do(%Plot3 = display(textplot([0,0,"Please provide a 3-component column vector to project"]),axes=none));return;end if; if Do(%RadioButton7) then Do(a = %MathContainer18); if type([a],'list'('Vector')) then A:=a; elif type([a],'list'('list'('Vector'))) then A:=op(a); elif type([a],'list'('set'('Vector'))) then A:=op(a); else Do(%MathContainer21 = MathML[Export]("Can't understand your entry for basis vectors. Please provide a sequence of two vectors."));return;end if; if nops([A])<>2 then Do(%MathContainer21 = MathML[Export]("Please provide exactly two independent basis vectors."));return;end if; if nops(select(type,indets([A]),name))<>0 or nops(select(type,indets(B),name))<>0 then Do(%Plot3 = display(textplot([0,0,"No graph can be drawn if vectors are not numeric"]),axes=none));return;end if; FIG := ProjectionPlot(B,[A], title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black], axes=box, showbasis, basisoptions=[color=blue], labels=[x,y,z]); Do(%Plot3 = FIG); else if Do(%ComboBox1)=[x,y,z] then X:=x;Y:=y;Z:=z;end if; if Do(%ComboBox1)=other then Do(temp=%MathContainer20);X:=temp[1];Y:=temp[2];Z:=temp[3];end if; Do(q1 = %MathContainer19); if is(q1=NULL) then Do(%MathContainer22=MathML[Export]("Provide equation of a plane thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y,Z},`subset`)=false then Do(%MathContainer21=MathML[Export]("Declared variables must match those in equation of plane"));return;end if; if eval(q2,[X=0,Y=0,Z=0])<>0 then Do(%MathContainer22=MathML[Export]("The plane does not pass thru origin")); else if nops(select(type,indets(B),name))<>0 then Do(%Plot3 = display(textplot([0,0,"No graph can be drawn if vectors are not numeric"]),axes=none));return;end if; FIG := ProjectionPlot(B,q2,[X,Y,Z], title="", complementoptions=[color=red], projectionoptions=[color=green], vectoroptions=[color=black],axes=box); Do(%Plot3 = FIG); end if; end if; end if; end module; end use; use DocumentTools in Do(%MathContainer17 = NULL); Do(%MathContainer22 = NULL); Do(%MathContainer18 = NULL); Do(%MathContainer19 = NULL); Do(%MathContainer21 = NULL); Do(%MathContainer20 = NULL); Do(%Plot3 = plots[display](plots[textplot]([0,0," "]),axes=none)); end use; 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use DocumentTools, Student[LinearAlgebra] in module() local a,B,A,BA,q1,q2,X,Y,Z,BN,N,temp; Do(B = %MathContainer17): if not type(B,Vector[column]) then Do(%MathContainer21 = MathML[Export]("Please provide a 3-component column vector to project"));return;end if; if Dimension(B)<>3 then Do(%MathContainer21 = MathML[Export]("Please provide a 3-component vector to project"));return;end if; if Do(%RadioButton7) then Do(a = %MathContainer18); if type([a],'list'('Vector')) then A:=a; elif type([a],'list'('list'('Vector'))) then A:=op(a); elif type([a],'list'('set'('Vector'))) then A:=op(a); else Do(%MathContainer21 = MathML[Export]("Can't understand your entry for basis vectors. Please provide a sequence of two vectors."));return;end if; if nops([A])<>2 then Do(%MathContainer21 = MathML[Export]("Please provide exactly two independent basis vectors."));return;end if; if Dimension(A[1])<>3 or Dimension(A[2])<>3 then Do(%MathContainer21 = MathML[Export]("Vectors must have exactly three components."));return;end if; if Equal(LinearAlgebra:-CrossProduct(A),<0,0,0>) then Do(%MathContainer21 = MathML[Export]("Basis vectors appear to be linearly dependent"));return;end if; M := <A[1]|A[2]>; P := M.(M^(%T).M)^(-1).M^(%T); BA := P.B; Do(%MathContainer21 = BA); else if Do(%ComboBox1)=[x,y,z] then X:=x;Y:=y;Z:=z;end if; if Do(%ComboBox1)=other then Do(temp=%MathContainer20);X:=temp[1];Y:=temp[2];Z:=temp[3];end if; Do(q1 = %MathContainer19); if is(q1=NULL) then Do(%MathContainer21=MathML[Export]("Provide equation of a plane thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y,Z},`subset`)=false then Do(%MathContainer21=MathML[Export]("Declared coordinates must match variables in equation of plane"));return;end if; if eval(q2,[X=0,Y=0,Z=0])<>0 then Do(%MathContainer21=MathML[Export]("The plane does not pass thru origin")); else N := Student[MultivariateCalculus][Gradient](q2,[X,Y,Z]); BN := (B.N)/(N.N)*N; BA := B-BN; Do(%MathContainer21 = BA); end if; end if; end if; end module; end use; use DocumentTools in module() local temp; try GetProperty(MathContainer21,expression); catch: return; end try; Do(temp = %MathContainer21); if nops([temp])=0 then return;end if; Do(%MathContainer21 = evalf(temp)); end module; end use; use DocumentTools, Student[LinearAlgebra] in module() local a,B,A,BA,q1,q2,X,Y,Z,BN,N,temp,BpA; Do(B = %MathContainer17): if not type(B,Vector[column]) then Do(%MathContainer22 = MathML[Export]("Please provide a 3-component column vector to project"));return;end if; if Dimension(B)<>3 then Do(%MathContainer22 = MathML[Export]("Please provide a 3-component vector to project"));return;end if; if Do(%RadioButton7) then Do(a = %MathContainer18); if type([a],'list'('Vector')) then A:=a; elif type([a],'list'('list'('Vector'))) then A:=op(a); elif type([a],'list'('set'('Vector'))) then A:=op(a); else Do(%MathContainer22 = MathML[Export]("Can't understand your entry for basis vectors. Please provide a sequence of two vectors."));return;end if; if nops([A])<>2 then Do(%MathContainer22 = MathML[Export]("Please provide exactly two independent basis vectors."));return;end if; if Dimension(A[1])<>3 or Dimension(A[2])<>3 then Do(%MathContainer22 = MathML[Export]("Vectors must have exactly three components."));return;end if; if Equal(LinearAlgebra[CrossProduct](A),<0,0,0>) then Do(%MathContainer22 = MathML[Export]("Basis vectors appear to be linearly dependent"));return;end if; M := <A[1]|A[2]>; P := M.(M^(%T).M)^(-1).M^(%T); BA := P.B; BpA := B-BA; Do(%MathContainer22 = BpA); else if Do(%ComboBox1)=[x,y,z] then X:=x;Y:=y;Z:=z;end if; if Do(%ComboBox1)=other then Do(temp=%MathContainer20);X:=temp[1];Y:=temp[2];Z:=temp[3];end if; Do(q1 = %MathContainer19); if is(q1=NULL) then Do(%MathContainer21=MathML[Export]("Provide equation of a plane thru origin")); else if type(q1,`=`) then q2:=lhs(q1)-rhs(q1); else q2:=q1;end if; if verify(indets(q2),{X,Y,Z},`subset`)=false then Do(%MathContainer22=MathML[Export]("Declared coordinates must match variables in equation of plane"));return;end if; if eval(q2,[X=0,Y=0,Z=0])<>0 then Do(%MathContainer22=MathML[Export]("The plane does not pass thru origin")); else N := Student[MultivariateCalculus][Gradient](q2,[X,Y,Z]); BN := (B.N)/(N.N)*N; Do(%MathContainer22 = BN); end if; end if; end if; end module; end use; use DocumentTools in module() local temp; try GetProperty(MathContainer22,expression); catch: return; end try; Do(temp = %MathContainer22); if nops([temp])=0 then return;end if; Do(%MathContainer22 = evalf(temp)); end module; end use; Table 14 Projection of a vector onto the plane spanned by a given basis JSFH The vector being projected is drawn in black; its component in the plane, in green; and its component orthogonal to the plane, in red. The basis vectors spanning the plane of projection are drawn in blue.

JSFH The VectorSumPlot command in the Student LinearAlgebra package will graph vectors and their sum, or show the parallelogram(s) of addition. The resultant vector is always drawn in black. The Vector Sum Plot task template provides a simplified interface to this command. After a list of either 2- or 3-dimensional vectors are entered, moving the slider that selects the number of vectors to add will cause both the resultant and the graph of the vectors to appear. Table 15 shows the task template applied to three vectors in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEoJiM4NDc3O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21uR0YkNiRRIjNGJ0Y1L0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y1. The vector sum is given analytically as the resultant; and graphically (in black), as the sum of the cyan, purple, and red vectors. We elected not to display the overlapping parallelograms of addition. JSFHJSFH Tools\342\211\273Tasks\342\211\273Browse: Linear Algebra\342\211\273Visualizations\342\211\273Vector Sum Plot Plot the Sum of Vectors Vectors (2 or more): Sum first LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTEY5use DocumentTools, Student[LinearAlgebra] in module() local N,Show,k,P,Z,Ln,Q; Do(N = %Slider2); Do(%Label6(caption) = N); if N>3 then Do(%CheckBox0 = false); Do(%CheckBox0(enabled)=false); else Do(%CheckBox0(enabled)=true);end if; if Do(%CheckBox0) then Show:=all else Show:=1; end if; Do(LL = %MathContainer23); if type([LL],'list'('Vector')) then L:=[LL]; elif type([LL],'list'('list'('Vector'))) then L:=LL; elif type([LL],'list'('set'('Vector'))) then Do(%MathContainer24 = MathML[Export]("List or sequence, but not a set of vectors")); else D(%MathContainer24 = MathML[Export]("Can't fathom your entry for vectors")); end if; if nops(L)=1 then Do(%MathContainer24 = MathML[Export]("Provide more than one vector"));return; elif nops(L)=0 then Do(%MathContainer24 = MathML[Export]("Provide at least two vectors"));return;;end if; n := min(N,nops(L)); if Dimension(L[1])=2 then Z:=<0,0> else Z:=<0,0,0>; end if; R := sum(L[k],k=1..n); if Dimension(Z)=2 then Q:=[x,y] else Q:=[x,y,z];end if; P := VectorSumPlot(Z,seq(L[k],k=1..n),show=Show,title="",labels=Q); Do(%MathContainer24 = R); Do(%Plot4 = P); end module; end use; = Resultant = 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use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. module() local N,Show,k,P,Z,Ln; Do(N = %Slider2); Do(%Label6(caption) = N); if N>3 then Do(%CheckBox0 = false); Do(%CheckBox0(enabled)=false); else Do(%CheckBox0(enabled)=true);end if; if Do(%CheckBox0) then Show:=all else Show:=1; end if; Do(LL = %MathContainer23); if type([LL],'list'('Vector')) then L:=[LL]; elif type([LL],'list'('list'('Vector'))) then L:=LL; elif type([LL],'list'('set'('Vector'))) then Do(%MathContainer24 = MathML[Export]("List or sequence, but not a set of vectors")); else D(%MathContainer24 = MathML[Export]("Can't fathom your entry for vectors")); end if; if nops(L)=1 then Do(%MathContainer24 = MathML[Export]("Provide more than one vector"));return; elif nops(L)=0 then Do(%MathContainer24 = MathML[Export]("Provide at least two vectors"));return;;end if; n := min(N,nops(L)); if LinearAlgebra[Dimension](L[1])=2 then Z:=<0,0> else Z:=<0,0,0>; end if; R := sum(L[k],k=1..n); P := Student[LinearAlgebra][VectorSumPlot](Z,seq(L[k],k=1..n),show=Show,title=""); Do(%MathContainer24 = R); Do(%Plot4 = P); end module; end use; LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNictSSNtaUdGJDYmUSJORicvJSVzaXplR1EjMTBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYuUSYmbGVxO0YnRjQvRjtRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYlUSIzRidGNEZBRjRGQUZBRkE= use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. Do(%MathContainer23 = NULL); Do(%MathContainer24 = NULL); Do(%Plot4 = plots[display](plots[textplot]([0,0,""]),axes=none)); Do(%CheckBox0 = false); Do(%Slider2(value) = 2); Do(%Label6(caption) = 2); end use; Table 15 The VectorSumPlot command accessed through the Vector Sum Plot task template JSFH

JSFH Legal Notice: \302\251 Maplesoft, a division of Waterloo Maple Inc. 2010. Maplesoft and Maple are trademarks of Waterloo Maple Inc. This application may contain errors and Maplesoft is not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact Maplesoft for permission if you wish to use this application in for-profit activities. JSFH Student[Calculus1][LimitTutor](); JSFH JSFH JSFH JSFH JSFH TTdSMApJNlJUQUJMRV9TQVZFLzE1MDQxOTg4MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiIiIiIyIiJDYi TTdSMApJNlJUQUJMRV9TQVZFLzE1MjM4NTY5MlgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCEiIyIiISIiIjYi TTdSMApJNlJUQUJMRV9TQVZFLzE1MjM4NTc2NFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiQiJCIiIyEiIiIiJTYi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= TTdSMApJNlJUQUJMRV9TQVZFLzE1MTc1NTc3NlgqJSlhbnl0aGluZ0c2Ii8lJ2Nvb3Jkc0clKmNhcnRlc2lhbkdbZ2whIyUhISEiJCIkLSUkY29zRzYjJSJ0Ry0lJHNpbkdGK0YsNiI=