Question

Помогите с матрица и Плиз

Answer 1

Ответ: во вложении Пошаговое объяснение:

Answer 2

$1)\; \; \left(\begin{array}{cccc}1&1&-1&|-2\\8&3&-6&|\; 12\\-4&-1\; &\; 3&|-9\end{array}\right)\sim \; \; 2*3str+2str\; ;\; 4*1str+3str\\\\\\\sim \left(\begin{array}{cccc}1&1&-1\;0&|-2\\0&1&0&|-6\\0&3&-1&|-17\end{array}\right)\sim \; \; \; 2str*(-3)+3str$

$\sim \left(\begin{array}{cccc}1&1&-1&|-1\\0 &1&\; 0&|-6\\0&0&-1&|\; \; \; 1\end{array}\right)\;\; \to \; \; \left\{\begin{array}{r}x+y-z=-2\\y=-6\\-z=1\end{array}\right\\\\\\z=-1\; ;\; \; y=-6\; ;\\\\x=-2+z-y=-2-1+6=3\\\\Otvet:\; \; x=3\; ,\; y=-6\; ,\; z=-1\; .$

$2)\; \; f(X)=4X^2+X-3\; ,\; \; X=A\cdot B\\\\X=A\cdot B=\left(\begin{array}{ccc}1&1&-1\\2&-1&1\end{array}\right)\cdot \left(\begin{array}{cc}1&2\\0&1\\0&1\end{array}\right)=\left(\begin{array}{cc}1&2\\2&4\end{array}\right)\\\\\\X^2=\left(\begin{array}{cc}1&2\\2&4\end{array}\right)\cdot \left(\begin{array}{cc}1&2\\2&4\end{array}\right)=\left(\begin{array}{cc}5&10\\10&20\end{array}\right)$

$f(X)=4\cdot \left(\begin{array}{cc}5&10\\10&20\end{array}\right)+ \left(\begin{array}{cc}1&2\\2&4\end{array}\right)-3\cdot \left(\begin{array}{cc}1&0\\0&1\end{array}\right)=\\\\\\=\left(\begin{array}{cc}20&40\\40&80\end{array}\right)+\left(\begin{array}{cc}1&2\\2&4\end{array}\right)-\left(\begin{array}{cc}3&0\\0&3\end{array}\right)= \left(\begin{array}{cc}18&42\\42&81\end{array}\right)$