Question

Матрица, 35 баллов, помогите срочно

Answer 1

Ответ:

$f(x)=x^2+4x-3E\ \ ,\ \ \ \ A=\left(\begin{array}{ccc}3&7&-2\\1&3&-3\\4&0&1\end{array}\right)\\\\\\A^2=\left(\begin{array}{ccc}3&7&-2\\1&3&-3\\4&0&1\end{array}\right)\cdot \left(\begin{array}{ccc}3&7&-2\\1&3&-3\\4&0&1\end{array}\right)=\left(\begin{array}{ccc}8&42&-29\\-6&16&-14\\16&28&-7\end{array}\right)$

$4\cdot A=4\cdot \left(\begin{array}{ccc}3&7&-2\\1&3&-3\\4&0&1\end{array}\right)=\left(\begin{array}{ccc}12&28&-8\\4&12&-12\\16&0&4\end{array}\right)$

$f(A)=\left(\begin{array}{ccc}8&42&-29\\-6&16&-14\\16&28&-7\end{array}\right)+\left(\begin{array}{ccc}12&28&-8\\4&12&-12\\16&0&4\end{array}\right)+\left(\begin{array}{ccc}-8&0&0\\0&-8&0\\0&0&-8\end{array}\right)=\\\\\\=\left(\begin{array}{ccc}12&70&-37\\-2&20&-26\\32&28&-11\end{array}\right)$