Question

Система Х1-2Х2+3X3+6 2X1-7X2-5X3=-2X X1-X2+X3=2

Answer 1

Метод Гаусса-Жордана:
$\left[\begin{array}{ccc|c|c}1&-2&3&6&\downarrow\\2&-7&-5&-2&-2\\1&-1&1&2&-1\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|c|c}1&-2&3&6&\\0&-3&-11&-14&\downarrow\\0&1&-2&-4&\uparrow\end{array}\right]\ \textgreater \ \\\left[\begin{array}{ccc|c|c}1&-2&3&6&2\\0&1&-2&-4&\updownarrow\\0&-3&-11&-14&3\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|c|c}1&0&-1&-2&\\0&1&-2&-4&\\0&0&-17&-26&:-17\end{array}\right]\ \textgreater \ \\\left[\begin{array}{ccc|c|c}1&0&-1&-2&1\\0&1&-2&-4&2\\0&0&1&\frac{26}{17}&\uparrow\end{array}\right]\ \textgreater$
$\left[\begin{array}{ccc|c|c}1&0&0&-\frac{8}{17}&\\0&1&0&-\frac{16}{17}&\\0&0&1&\frac{26}{17}&\end{array}\right]$

$\left[\begin{array}{c}x_1\\x_2\\x_3\end{array}\right]=\left[\begin{array}{c}-\frac{8}{17}\\-\frac{16}{17}\\\frac{26}{17}\end{array}\right]$