{-2х1+х2-х3=8 -3х1-х2+2х3=11 -2х1+х2+2х3=-3 метод крамера

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firsova5911

02.07.2020

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vipppp19743355

02.07.2020

$\begin{cases}-2x_1+x_2-x_3=8\\-3x_1-x_2+2x_3=11\\-2x_1+x_2+2x_3=-3\end{cases}\\\mathcal4= \left[\begin{array}{ccc}-2&1&-1\\-3&-1&2\\-2&1&2\end{array}\right]=4-4+3+2+4+6=15\\\mathcal4_{x_1}= \left[\begin{array}{ccc}8&1&-1\\11&-1&2\\-3&1&2\end{array}\right]=-16-6-11+3-22-16=-68\\\mathcal4_{x_2}=\left[\begin{array}{ccc}-2&8&-1\\-3&11&2\\-2&-3&2\end{array}\right]=-44-32-9-22+48-12=-71\\\mathcal4_{x_3}=\left[\begin{array}{ccc}-2&1&8\\-3&-1&11\\-2&1&-3\end{array}\right]=-6-22-24-16-9+22=-55$

$x_1=\frac{\mathcal4{x_1}}{\mathcal4}=-\frac{68}{15}\ ;x_2=\frac{\mathcal4{x_2}}{\mathcal4}=-\frac{71}{15}\ ;x_3=\frac{\mathcal4{x_3}}{\mathcal4}=-\frac{55}{15}=-\frac{11}{3}$

Проверка:
$\begin{cases}\frac{2*68}{15}-\frac{71}{15}+\frac{55}{15}=8\\\frac{3*68}{15}+\frac{71}{15}-\frac{2*55}{15}=11\\\frac{2*68}{15}-\frac{71}{15}-\frac{2*55}{15}=-3\end{cases}=\ \textgreater \ \begin{cases}8=8\\11=11\\-3=-3\end{cases}$