Solution of Linear Equations by Gaussian Elimination and Back-Substitution

Initialise

Clear the workspace and load Linear Algebra package

> restart;

> with(LinearAlgebra):

If you want practice at hand calculation you should use the worksheet "Interactive Gaussian Elimination" (see Menu)

Enter the matrix of coefficients and right-hand side vector

You may edit the following statements or use the matrix and vector pallettes to enter new data ( see View, Palettes)

> A:=<<4 | 2 | 3 | 2> , <8 | 3 | -4 | 7> , <4 | -6 | 2 | -5>>;

> b:=<<15, 7, 6>>;

Form the augmented matrix and solve

The Maple routine GaussianElimination requires the augmented matrix A|b as input.

In this worksheet this matrix is called Ab and is formed using <A|b>

> Ab:=<A|b>;

The row echelon form H|c (here called Hc) of Ab is computed by GaussianElimination.

(For a square system of equations the row echelon form of A is upper triangular )

Note that the Maple function GaussianElimination performs a systematic version of the idea of elementary row operations:

(i) Multiples of R1 are subtracted from R2, R3 . . Rn to reduce the elements below the leading diagonal in the first column to zero.

(ii) In the resulting system multiples of R2 are subtracted from R3, R4 . . Rn to reduce the elements below the leading diagonal in the second column to zero.

(iii) This process