Linear system
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*}