## Matlab Tutorial 5: Linear Equations

In this Matlab tutorial we will deal with linear equations, the least square method, condition numbers over & under-determined equations.

Let’s start with an example.

Example 1

We have an equation system with three unknown variables and three equations. What will be the solution to the system below?

3w-2y+4z=8
5w+8y-6z=-5
9w-2y+7z=-17

Assume a matrix A containing the coefficients multiplied with x, y and z, and a vector with the numbers on the right-hand side of the equations. We can thus rewrite our equations as:

AX=b , where X contains the unknown (w, y and z), A and b are shown below.

```b= A= 8 3 -2 4 -5 5 8 -6 -17 9 -2 7```

How will we find the solution?

`>> X=inv(A)*b`

or

`>> X=A\b`

both gives a correct answer. The last method produces a Gaussian elimination if A is a quadratic matrix. In our case X becomes:

```X= -36.7778 71.2778 65.2222```

This is no exact solution, only an approximation. Try also a specific command: Read more »