Gaussian Elimination

Basic form: $A \cdot x = b$.

An example:

$$A = \left[\begin{array} {cccc} 6 & -2 & 2 & 4 \ 12 & -8 ... ...0 \ 3 & -13 & 9 & 3 \ -6 & 4 & 1 & -18 \end{array} \right],$$

$$x = \left[\begin{array} {c} x_1 \ x_2 \ x_3 \ x_4 \end{array} \right],$$

$$b = \left[\begin{array} {c} 12 \ 34 \ 27 \ -38 \end{array} \right].$$

1.

Eliminate x₁ in equations 2,3 and 4

2.

Eliminate x₂ in equations 3 and 4

3.

Eliminate x₃ in equation 4

4.

Solve the above system starting from the last equation