Решите систему линейных уровнени по формулам Крамера x+y-2z=1 2x+3y+z=0 x-2y-z=7

Решите задачу:

$\Delta = \left|\begin{array}{ccc}1&1&-2\\2&3&1\\1&-2&-1\end{array}\right|= \left|\begin{array}{cc}3&1\\-2&-1\end{array}\right|- \left|\begin{array}{cc}2&1\\1&-1\end{array}\right|-2 \left|\begin{array}{cc}2&3\\1&-2\end{array}\right| =\\\\\\=(-3+2)-(-2-1)-2(-4-3)=16\ne 0\\\\\Delta _{x}= \left|\begin{array}{ccc}1&1&-2\\0&3&1\\7&-2&-1\end{array}\right|=(-3+2)-(0-7)-2(0-21)=48\\\\\\\Delta _{y}=\left|\begin{array}{ccc}1&1&-2\\2&0&1\\1&7&-1\end{array}\right|=(0-7)-(-2-1)-2(14-0)=-32$

$\Delta _{z}=\left|\begin{array}{ccc}1&1&1\\2&3&0\\1&-2&7\end{array}\right|=(21-0)-(14-0)+(-4-3)=0\\\\\\x= \frac{\Delta _{x}}{\Delta }=\frac{48}{16}=3\\\\y=\frac{\Delta _{y}}{\Delta }=\frac{-32}{16}=-2\\\\z=\frac{\Delta _{z}}{\Delta }=\frac{0}{16}=0$