\documentclass[12pt]{scrartcl}

\usepackage{amsmath}

\DeclareMathOperator{\diag}{diag}
\renewcommand*{\vec}[1]{\boldsymbol{#1}}

\begin{document}

The set of linear equations:
\[
a_ix_i = b_i  \qquad \forall i=1, \ldots, n
\]
can be written as a matrix equation:
\[
\diag(\vec{a})\vec{x} = \vec{b}
\]
where $\vec{x} = (x_1, \ldots, x_n)^T$, $\vec{b} = (b_1, \ldots, b_n)^T$
and
\[
\diag(\vec{a}) = 
\begin{bmatrix}
a_1 & 0 & \cdots & 0\\
0 & a_2 & \ddots & \vdots\\
\vdots & \ddots & \ddots & 0\\
0 & \cdots & 0 & a_n
\end{bmatrix}
\]

\end{document}
