BackSubstitution
Solves a system of linear equations by means of back substitution.
Syntax
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BackSubstitution(A, y)-
Ais an upper triangularn×nmatrix -
yis ann-dimensional matrix
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Description
If A is an upper triangular matrix of size n×n and y an n-dimensional vector, then BackSubstitution(A, y) solves the matrix equation A⋅x = y for x using back substitution.
If A isn’t square or if y isn’t of the right dimension, an error is generated. An error is also generated if A is singular. However, if non of these conditions apply but A isn’t upper triangular, a vector is returned, but it is not guaranteed to solve the equation.
Examples
A ≔ ❨❨2, 1, 0, 3❩, ❨0, 1, 4, 2❩, ❨0, 0, 1, 1❩, ❨0, 0, 0, 1❩❩
⎛2 1 0 3⎞ ⎜0 1 4 2⎟ ⎜0 0 1 1⎟ ⎝0 0 0 1⎠
y ≔ ❨5, −2, 0, 1❩
⎛5 ⎞ ⎜−2⎟ e⎜0 ⎟ ⎝1 ⎠
x ≔ BackSubstitution(A, y)
⎛1 ⎞ ⎜0 ⎟ e⎜−1⎟ ⎝1 ⎠
A⋅x
⎛5 ⎞ ⎜−2⎟ e⎜0 ⎟ ⎝1 ⎠