NumericalMethods[BackSubstitute] - solves U . X = b, where U is an upper-triangular regular matrix
NumericalMethods[ForwSubstitute] - solves L . X = b, where L is a lower-triangular regular matrix

Calling Sequence
    BackSubstitute(A)
    ForwSubstitute(A)

Parameters
    A - matrix; an n by n+1 matrix, <U|b> for BackSubstitute, <L|b> for ForwSubstitute.

Description
The BackSubstitute and ForwSubstitute commands solve regular systems of linear equations by back and forward substitution, respectively. They provide basic funtionality to accompany the MatrixEliminate command when a user does not wish to use the more powerful commands from the LinearAlgebra package. One possible reason is that they are implemented in the same way as the MatrixEliminate command, thus offering a (rough) direct comparison of performance (computational complexity) of these two algorithms.

This command is part of the NumericalMethods package, so it can be used in the form BackSubstitute(..) only after executing the command with(NumericalMethods). However, it can always be accessed through the long form of the command by using NumericalMethods[BackSubstitute](..).

Examples

> A:=<<2,0>|<1,1>|<-1,1>>;

A := Matrix([[2, 1, -1], [0, 1, 1]])

> BackSubstitute(A);

Vector[column]([[-1], [1]])

> ForwSubstitute(A);
Error, (in NumericalMethods:-ForwSubstitute) The matrix must be lower triangular.