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Student[LinearAlgebra]

 LinearSolve
 solve the linear equations A . x = b

 Calling Sequence LinearSolve(A, b, options)

Parameters

 A - Matrix or list b - (optional) column Vector options - (optional) parameters; for a complete list, see LinearAlgebra[LinearSolve]

Description

 • The LinearSolve command returns the Vector x that satisfies the linear system $A·x=b$.
 If b is omitted, then the linear system is interpreted from the first argument, which is taken to be the augmented Matrix in which the last column provides the right-hand side data.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $A≔⟨⟨1,2,3⟩|⟨4,5,6⟩|⟨7,8,0⟩⟩:$
 > $b≔⟨3,2,-2⟩:$
 > $\mathrm{LinearSolve}\left(A,b\right)$
 $\left[\begin{array}{c}{-2}\\ \frac{{2}}{{3}}\\ \frac{{1}}{{3}}\end{array}\right]$ (1)
 > $M≔⟨⟨1,1,1,4⟩|⟨1,1,-2,1⟩|⟨3,1,1,8⟩|⟨-1,1,-1,-1⟩|⟨0,1,1,0⟩⟩:$
 > $\mathrm{M_sol}≔\mathrm{LinearSolve}\left(M\right)$
 ${\mathrm{M_sol}}{≔}\left[\begin{array}{c}\frac{{25}}{{6}}\\ \frac{{4}}{{3}}\\ {-}\frac{{5}}{{2}}\\ {-2}\end{array}\right]$ (2)
 > $M\left[1..-1,1..-2\right]·\mathrm{M_sol}=M\left[1..-1,-1\right]$
 $\left[\begin{array}{c}{0}\\ {1}\\ {1}\\ {0}\end{array}\right]{=}\left[\begin{array}{c}{0}\\ {1}\\ {1}\\ {0}\end{array}\right]$ (3)
 > $R≔⟨⟨1,2,3⟩|⟨4,5,7⟩|⟨7,8,9⟩|⟨10,11,12⟩⟩:$
 > $z≔⟨3,2,0⟩:$
 > $\mathrm{LinearSolve}\left(R,z\right)$
 $\left[\begin{array}{c}{-}\frac{{7}}{{6}}{+}\frac{{{\mathrm{_t1}}}_{{4}}}{{2}}\\ {-1}\\ \frac{{7}}{{6}}{-}\frac{{3}{}{{\mathrm{_t1}}}_{{4}}}{{2}}\\ {{\mathrm{_t1}}}_{{4}}\end{array}\right]$ (4)