Найти определитель матричным методом Методом Крамера Метод Гауса

Question 1

Найти определитель матричным методом
Методом Крамера
Метод Гауса

Question 2

1)Матричный метод:
$AX=B\\A^{-1}AX=A^{-1}B\\X=A^{-1}B$
$\left[\begin{array}{ccc|ccc|c}2&-1&2&1&0&0&:2\\1&1&2&0&1&0\\4&1&4&0&0&1\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&\downarrow\\1&1&2&0&1&0&-1\\4&1&4&0&0&1&-4\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&\\0&1,5&1&-0,5&1&0&*\frac{2}{3}\\0&3&0&-2&0&1&\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|ccc|c}1&-0,5&1&0,5&0&0&0,5\\0&1&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&0&\updownarrow\\0&3&0&-2&0&1&-3\end{array}\right]\textgreater \$
$\left[\begin{array}{ccc|ccc|c}1&0&\frac{4}{3}&\frac{1}{3}&\frac{1}{3}&0&\\0&1&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&0&\\0&0&-2&-1&-2&1&:-2\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|ccc|c}1&0&\frac{4}{3}&\frac{1}{3}&\frac{1}{3}&0&-\frac{4}{3}\\0&1&\frac{2}{3}&-\frac{1}{3}&\frac{2}{3}&0&-\frac{2}{3}\\0&0&1&\frac{1}{2}&1&-\frac{1}{2}&\uparrow\end{array}\right]\ \textgreater \ \\\ \textgreater \$
$\left[\begin{array}{ccc|ccc|c}1&0&0&-\frac{1}{3}&-1&\frac{2}{3}&\\0&1&0&-\frac{2}{3}&0&\frac{1}{3}&\\0&0&1&\frac{1}{2}&1&-\frac{1}{2}&\end{array}\right]$
$\left[\begin{array}{ccc}-\frac{1}{3}&-1&\frac{2}{3}\\-\frac{2}{3}&0&\frac{1}{3}\\\frac{1}{2}&1&-\frac{1}{2}&\end{array}\right]* \left[\begin{array}{c}3\\-4\\-3\end{array}\right] =\left[\begin{array}{c}-1+4-2\\-2-1\\\frac{3}{2}-4+\frac{3}{2}\end{array}\right]=\left[\begin{array}{c}1\\-3\\-1\end{array}\right]$
2)Метод Крамера:(вложение)
3)Метод Гаусса:
$\left[\begin{array}{ccc|c|c}2&-1&2&3&\downarrow\\1&1&2&-4&\uparrow\\4&1&4&-3&\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|c|c}1&1&2&-4&\downarrow\\2&-1&2&3&-2\\4&1&4&-3&-4\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|c|c}1&1&2&-4&\\0&-3&-2&11&:-3\\0&-3&-4&13&\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|c|c}1&1&2&-4&\\0&1&\frac{2}{3}&-\frac{11}{3}&\\0&-3&-4&13&\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|c|c}1&1&2&-4&-1\\0&1&\frac{2}{3}&-\frac{11}{3}&\updownarrow\\0&-3&-4&13&3\end{array}\right]\ \textgreater \$
$\left[\begin{array}{ccc|c|c}1&1&2&-4&-1\\0&1&\frac{2}{3}&-\frac{11}{3}&\updownarrow\\0&-3&-4&13&3\end{array}\right]\ \textgreater \ \left[\begin{array}{ccc|c|c}1&0&\frac{4}{3}&-\frac{1}{3}&\\0&1&\frac{2}{3}&-\frac{11}{3}&\\0&0&-2&2&:-2\end{array}\right]\ \textgreater \ \\\ \textgreater \ \left[\begin{array}{ccc|c|c}1&0&\frac{4}{3}&-\frac{1}{3}&-\frac{4}{3}\\0&1&\frac{2}{3}&-\frac{11}{3}&-\frac{2}{3}\\0&0&1&-1&\uparrow\end{array}\right]\ \textgreater \$
$\left[\begin{array}{ccc|c|c}1&0&0&1&\\0&1&0&-3&\\0&0&1&-1&\end{array}\right]$