# [Maxima] Gaussian Elimination Help

Alexey Beshenov al at beshenov.ru
Mon Aug 11 01:45:07 CDT 2008

On Monday 11 August 2008 10:06:23 Angelique Sta maria wrote:
> How do you program Gaussian Elimination in Maxima?
>
> Can you please guide me doing the program?

Check the first sections of the Maxima Manual as well as sections on matrices,
function definition, and program flow.

http://maxima.sourceforge.net/docs/manual/en/maxima.html

If you just need to solve linear equations,
check 'solve', 'linsolve', 'fast_linsolve', etc.

http://beshenov.ru/maxima/faq.html#Matrices_and_Linear_Algebra

> How do you solve for the x's (variables) using backward substitution in
> gaussian elimination?

See a linear algebra textbook.

x_n = b_n,
x_{n-1} = b_{n-1} - a_{n-1,n} x_n
x_{n-2} = b_{n-2} - a_{n-2,n} x_n - a_{n-2,n-1} x_{n-1}
...

In case of elimination with full pivoting, apply a corresponding inverse
permutation for x_1, x_2, ..., x_n.

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Alexey Beshenov http://beshenov.ru/