$$\large{\displaylines{\normalsize\begin{array}{l|l}
1 & \left(\begin{array}{ccc|c}1&3&-2&5\\3&5&6&7\\2&4&3&8\end{array}\right)\\ \\
2 & \left(\begin{array}{ccc|c}\color{#ff7800}1&\color{#ff7800}3&\color{#ff7800}-2&\color{#ff7800}5\\0&\color{#ff7800}1&\color{#ff7800}-3&\color{#ff7800}2\\0&0&\color{#ff7800}1&\color{#ff7800}2\end{array}\right)\\ \\
3 & \left(\begin{array}{ccc|c}\color{#ff7800}1&0&0&\color{#ff7800}-15\\0&\color{#ff7800}1&0&\color{#ff7800}8\\0&0&\color{#ff7800}1&\color{#ff7800}2\end{array}\right)\\ \\
4 & \begin{cases}\color{#ff7800}x=-15\\ \color{#FF7800}y=8\\ \color{#ff7800}z=2\end{cases}\\ \\
\end{array}}}$$
Решение системы линейных уравнений методом Гаусса — Жордана
Расширенная матрица в каноническом виде