Question

x1+x2+x3=2 2x1-3x2+2x3=2 3x1-2x2+4x3=-5 как решить?

Answer 1

Метод Гаусса-Жордана
$(A|B)rightarrow(E|X)\begin{cases}x_1+x_2+x_3=2\2x_1-3x_2+2x_3=2\3x_1-2x_2+4x_3=-5end{cases}$
$left(begin{array}{ccc|c|c}1&1&1&2&downarrow\2&-3&2&2&-2\3&-2&4&-5&-3end{array}right) textgreater left(begin{array}{ccc|c|c}1&1&1&2&\0&-5&0&-2&:-5\0&-5&1&-11&end{array}right) textgreater \left(begin{array}{ccc|c|c}1&1&1&2&-1\0&1&0&frac{2}{5}&updownarrow\0&-5&1&-11&5end{array}right) textgreater left(begin{array}{ccc|c|c}1&0&1&frac{8}{5}&-1\0&1&0&frac{2}{5}&\0&0&1&-9&uparrowend{array}right) textgreater \left(begin{array}{ccc|c|c}1&0&0&frac{53}{5}&\0&1&0&frac{2}{5}&\0&0&1&-9&end{array}right)$
$X=left(begin{array}{c}x_1\x_2\x_3end{array}right)=left(begin{array}{c}frac{53}{5}\frac{2}{5}\-9end{array}right)$