A set of \(m \geq 1\) linear equations in \(n\) variables,
\[\begin{equation*}
\begin{cases}
a_{11} x_1 + a_{12} x_2 + a_{13} x_3 + \cdots + a_{1n} x_n = b_1 \\
a_{21} x_1 + a_{22} x_2 + a_{23} x_3 + \cdots + a_{2n} x_n = b_2 \\
a_{31} x_1 + a_{32} x_2 + a_{33} x_3 + \cdots + a_{3n} x_n = b_3 \\
\vdots \\
a_{m1} x_1 + a_{m2} x_2 + a_{m3} x_3 + \cdots + a_{mn} x_n = b_m.
\end{cases}
\end{equation*}
\]