$$ \begin{cases} a_{11}x_{1}+a_{12}x_{2}+\cdots+a_{1n}x_{n}=b_{1}\\ a_{21}x_{1}+a_{22}x_{2}+\cdots+a_{2n}x_{n}=b_{2}\\ \vdots\\ a_{m1}x_{1}+a_{m2}x_{2}+\cdots+a_{mn}x_{n}=b_{n} \end{cases} $$

$$ \begin{bmatrix} a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn} \end{bmatrix} $$

$$ \begin{bmatrix} a_{11}&a_{12}&\cdots&a_{1n}&\,&b_{1}\\ a_{21}&a_{22}&\cdots&a_{2n}&\,&b_{2}\\ \vdots&\vdots&\ddots&\vdots&&\vdots\\ a_{m1}&a_{m2}&\cdots&a_{mn}&\,&b_{n} \end{bmatrix} $$