Question

Найти матрицу С^-1,обратную матрице С=AB^T+3E

Answer 1

$A=\left(\begin{array}{cc}1&2\\3&4\\5&6\end{array}\right)\; \; ,\; \; B=\left(\begin{array}{cc}2&0\\5&4\\1&2\end{array}\right)\; \; \to \; \; B^{T}=\left(\begin{array}{ccc}2&5&1\\0&4&2\end{array}\right)\\\\\\A\cdot B^{T}=\left(\begin{array}{ccc}2&13&5\\6&31&11\\10&49&17\end{array}\right)\\\\\\C=A\cdot B^{T}+3E=\left(\begin{array}{ccc}2&13&5\\6&31&11\\10&49&17\end{array}\right)+\left(\begin{array}{ccc}3&0&0\\0&3&0\\0&0&3\end{array}\right)=\left(\begin{array}{ccc}5&13&5\\6&34&11\\10&49&20\end{array}\right)$