ForwardSubstitution
Solves a system of linear equations by means of forward substitution.
Syntax

ForwardSubstitution(A, y)

A
is a lower triangularn×n
matrix 
y
is ann
dimensional matrix

Description
If A
is a lower triangular matrix of size n×n
and y
an n
dimensional vector, then ForwardSubstitution(A, y)
solves the matrix equation A⋅x = y
for x
using forward 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 lower triangular, a vector is returned, but it is not guaranteed to solve the equation.
Examples
A ≔ ❨❨2, 0, 0, 0❩, ❨1, 5, 0, 0❩, ❨3, 0, 1, 0❩, ❨1, 3, 2, 1❩❩
⎛2 0 0 0⎞ ⎜1 5 0 0⎟ ⎜3 0 1 0⎟ ⎝1 3 2 1⎠
y ≔ ❨2, 6, 5, 6❩
⎛2⎞ ⎜6⎟ e⎜5⎟ ⎝6⎠
x ≔ ForwardSubstitution(A, y)
⎛1 ⎞ ⎜1 ⎟ e⎜2 ⎟ ⎝−2⎠
A⋅x
⎛2⎞ ⎜6⎟ e⎜5⎟ ⎝6⎠