# Overview

In this tutorial, we will learn how to solve linear algebraic equations using Octave software. We will use the Gaussian elimination to solve the system of equations.

## Example

Let’s solve the following system of three linear equations. The unknowns are x, y, and z.

4x + 3y + 2z = 44

3x + 7y + 4z = 60

8x + 9y + 5z = 101

We will define three matrices so that we can represent the equations in matrix form:

Ax = b

where A, x, and b are matrices.

To solve the unknowns, we need to solve for x. Let’s write the linear equations in the form:

*x = A\b*

## Octave Code

*>> % Define A*

*>> A = [4 3 2;3 7 4;8 9 5];*

*>> % Define b*

*>> b = [44; 60; 101];*

*>> x = A\b*

*x =*

*6*

*2*

*7*

*>>*

It is clear that the solution is

x = 6

y = 2

z = 7

Alternatively, we can use the inverse matrix of A using the *inv()* function.

x = inv(A)*b

Note that the *inv()* function is slow and inaccurate for a large set of equations.

We can verify the solution by computing the

*A*x – b*

The result should be close to zero.

*>> format bank*

*>> A*x -b*

*ans =*

*0.00*

*0.00*

*0.00*

—

## Octave Tutorials

Octave Tutorial on this website can be found at:

https://www.testingdocs.com/octave-tutorial/

More information on Octave can be found on the official website:

https://www.gnu.org/software/octave/index