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Student[NumericalAnalysis][BackSubstitution] - solve A.x = b where A is an upper-triangular matrix
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Calling Sequence
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BackSubstitution(A, b)
BackSubstitution(A)
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Parameters
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A
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Matrix; an upper-triangular  matrix or an augmented (A|b)  matrix where 
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b
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(optional) Vector; a vector of length 
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Description
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The BackSubstitution command returns a solution to the equation A.x=b, where A is an upper-triangular matrix, using the back substitution algorithm.
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Examples
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![with(Student[NumericalAnalysis])](/support/helpjp/helpview.aspx?si=4323/file05064/math78.png)
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![A := Matrix([[1.1, 4.9, 7.7], [4.4, 7.5, 8.1], [2.7, 8, 10]])](/support/helpjp/helpview.aspx?si=4323/file05064/math82.png)
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![A := Matrix([[1.1, 4.9, 7.7], [4.4, 7.5, 8.1], [2.7, 8, 10]])](/support/helpjp/helpview.aspx?si=4323/file05064/math85.png)
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![b := Vector([3.4, 5.4, 3.3])](/support/helpjp/helpview.aspx?si=4323/file05064/math89.png)
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](/support/helpjp/helpview.aspx?si=4323/file05064/math92.png)
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![Lower, Upper := MatrixDecomposition(A, method = LU, output = ['L', 'U'])](/support/helpjp/helpview.aspx?si=4323/file05064/math96.png)
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![Lower, Upper := Matrix([[1, 0, 0], [4.000000000, 1, 0], [2.454545455, .3328324570, 1]]), Matrix([[1.1, 4.9, 7.7], [0, -12.10000000, -22.70000000], [0, 0, -1.344703226]])](/support/helpjp/helpview.aspx?si=4323/file05064/math99.png)
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](/support/helpjp/helpview.aspx?si=4323/file05064/math106.png)
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 = Vector[column]([[2.409319491], [-2.553749034], [1.722482965]])](/support/helpjp/helpview.aspx?si=4323/file05064/math113.png)
| (5) |
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