A system of linear equations, for example,
$$ \begin{cases} 5 x_1 + 2 x_2 = 4\\ 3 x_1 + 6 x_2 = 7 \end{cases} $$
can be written down using matrix notation in the following way:
$$ \begin{pmatrix} 5 & 2\\ 3 & 6 \end{pmatrix} \begin{pmatrix} x_1\\ x_2 \end{pmatrix} = \begin{pmatrix} 4\\ 7 \end{pmatrix} $$
Using such a matrix notation is a standard way of solving systems of linear equation by computer algebra systems both symbolically (e.g., Wolfram Mathematica, Sage) and numerically (e.g., R, MathLab).
In the following lessons we will discuss in details how it works.