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# Exercise 24: More Mathematics (Solution)

This is the solution to Exercise 24.
\documentclass[11pt]{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}

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