Question

Найти значение многочлена f(A) от матрицы А:
f(x) = 7x^2+2x-4, A= (-1 8)
(2 -1)

Answer 1

$f(x)=7x^2+2x-4\\\\A^2=\left(\begin{array}{cc}-1&8\\2&-1\end{array}\right)\cdot \left(\begin{array}{cc}-1&8\\2&-1\end{array}\right)=\left(\begin{array}{cc}17&-16\\-4&17\end{array}\right)\\\\\\7A^2=7\cdot \left(\begin{array}{cc}17&-16\\-4&17\end{array}\right)=\left(\begin{array}{cc}119&-112\\-28&119\end{array}\right)\\\\\\2A=2\cdot \left(\begin{array}{cc}-1&8\\2&-1\end{array}\right)=\left(\begin{array}{cc}-2&16\\48&-2\end{array}\right)$

$-4E=-4\cdot \left(\begin{array}{cc}1&0\\0&1\end{array}\right)=\left(\begin{array}{cc}-4&0\\0&-4\end{array}\right)=$

$f(A)=\left(\begin{array}{cc}119&-112\\-28&119\end{array}\right)+\left(\begin{array}{cc}-2&16\\4&-2\end{array}\right)-\left(\begin{array}{cc}-4&0\\0&-4\end{array}\right)=\\\\\\=\left(\begin{array}{cc}121&-96\\-24&121\end{array}\right)$