Решить СЛАУ методом гаусса 4х+у+2z =6 x+3y-z=12 2x+5y+z=3

Решите задачу:

$\left\{\begin{array}{c}4x+y+2z=6\\x+3y-z=12\\2x+5y+z=3\end{array}\right \\\\\\ \left(\begin{array}{ccc}4&1&2\;\; |\, 6\\1&3&-1\, |\, 12\\2&5&1\;\, |\, 3\end{array}\right)\sim \left(\begin{array}{cccc}1&3&-1&|\; \; \; 12\\0&-1&3&| -21\\0&-11&6&|-42\end{array}\right)\sim \\\\\\ \sim \left(\begin{array}{cccc}1&3&-1&|\; \; \; 12\\0&-1&3&|-21\\0&0&-27&|\; \; 189\end{array}\right)$

$\left\{\begin{array}{c}x+3y-z=12\\-y+3z=-21\\-27z=189\end{array}\right \; \; \; \left\{\begin{array}{c}x+3y-z=12\\-y=-21-3\cdot (-7)\\z=-7\end{array}\right\; \; \left\{\begin{array}{c}x=12-3\cdot 0-7\\y=0\\z=-7\end{array}\right$

$\left\{\begin{array}{c}x=5\\y=0\\z=-7\end{array}\right$