Question

Решить уравнение методом Крамера
2x-7y+z=-4
3x+y-z=17
x-y+3z=3

Answer 1

$left{begin{array}{ccc}2x-7y+z=-4\3x+y-z=17\x-y+3z=3end{array}right\\W= left|begin{array}{ccc}2&-7&1\3&1&-1\1&-1&3end{array}right|=6-3+7-1-2+63=70\\W_x=left|begin{array}{ccc}-4&-7&1\17&1&-1\3&-1&3end{array}right|=-12+21-17-3+4+357=350\\W_y=left|begin{array}{ccc}2&-4&1\3&17&-1\1&3&3end{array}right|=102+9+4-17+6+36=140$

$W_z=left|begin{array}{ccc}2&-7&-4\3&1&17\1&-1&3end{array}right|=6-119+12+4+34+63=0$

$left{begin{array}{ccc}x=frac{W_x}{W}\y=frac{W_y}{W}\z=frac{W_z}{W}end{array}rightRightarrow left{begin{array}{ccc}x=frac{350}{70}\y=frac{140}{70}\z=frac{0}{70}end{array}rightRightarrow left{begin{array}{ccc}x=5\y=2\z=0end{array}right$