BackSubstitution
Solves a system of linear equations by means of back substitution.
Syntax

BackSubstitution(A, y)

A
is an upper triangularn×n
matrix 
y
is ann
dimensional matrix

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 ⎠