Matrix Definition

An $n\times m$ matrix has $n$ rows and $m$ columns

$$\left[\begin{array}{ccc}{a}_{11}& \cdots & a_{1m}\\ ⋮& \ddots & ⋮\\ a_{n1}& \cdots & a_{nm}\end{array}\right]$$

A system of linear equation’s coefficient matrix would have $n$ equations and $m$ variables