Consider the system of linear equations from Example NSLE.
\begin{align*} 2x_1+4x_2-3x_3+5x_4+x_5&=9\\ 3x_1+x_2+x_4-3x_5&=0\\ -2x_1+7x_2-5x_3+2x_4+2x_5&=-3 \end{align*} has coefficient matrix and vector of constants \begin{align*} A&= \begin{bmatrix} 2 & 4 & -3 & 5 & 1\\ 3 & 1 & 0 & 1 & -3\\ -2 & 7 & -5 & 2 & 2 \end{bmatrix} &\vect{b}&=\colvector{9\\0\\-3} \end{align*} and so will be described compactly by the vector equation $A\vect{x}=\vect{b}$.