Question

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

Answer 1

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

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

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