Метод Крамера.
[tex]\Delta =\left[\begin{array}{ccc}1&2&0\\3&2&1\\0&1&2\end{array}\right]=-9[/tex]
[tex]\Delta_1=\left[\begin{array}{ccc}10&2&0\\23&2&1\\13&1&2\end{array}\right]=-36[/tex]
[tex]\Delta_2=\left[\begin{array}{ccc}1&10&0\\3&23&1\\0&13&2\end{array}\right]=-27[/tex]
[tex]\Delta_3 =\left[\begin{array}{ccc}1&2&10\\3&2&23\\0&1&13\end{array}\right]=-45[/tex]
[tex]x=\frac{\Delta_1}{\Delta}=\frac{-36}{-9}=4; y=\frac{\Delta_2}{\Delta}=\frac{-27}{-9}=3; z=\frac{\Delta_3}{\Delta}=\frac{-45}{-9}=5;[/tex]
Метод Жордана-Гаусса.
[tex]\left(\begin{array}{ccc|c}1&2&0&10\\3&2&1&23\\0&1&2&13\end{array}\right)= \\ \left(\begin{array}{ccc|c}1&2&0&10\\0&-4&1&-7\\0&1&2&13\end{array}\right)= \\ \left(\begin{array}{ccc|c}1&0&-4&-16\\0&1&2&13\\0&0&9&45\end{array}\right)= \\ \left(\begin{array}{ccc|c}1&0&-4&-16\\0&1&2&13\\0&0&1&5\end{array}\right)= \\ \left(\begin{array}{ccc|c}1&0&0&4\\0&1&0&3\\0&0&1&5\end{array}\right)= \\ [/tex]
x=4, y=3, z=5
Матричный метод.
[tex]A=\left(\begin{array}{ccc}1&2&0\\3&2&1\\0&1&2\end{array}\right), \Delta A=-9, B=\left(\begin{array}{c}10&23&13\end{array}\right)[/tex]
[tex]A^{-1}=-\frac{1}{9}\left(\begin{array}{ccc}3&-4&2\\-6&2&-1\\3&-1&-4\end{array}\right)[/tex]
[tex]-\frac{1}{9}\left(\begin{array}{ccc}3&-4&2\\-6&2&-1\\3&-1&-4\end{array}\right) \cdot \left(\begin{array}{c}10&23&13\end{array}\right)=-\frac{1}{9}\left(\begin{array}{c}-36\\-27\\-45\end{array}\right)=\left(\begin{array}{c}4\\3\\5\end{array}\right)[/tex]
