Question

Помогите решить матрицы
M=3
N=7

Answer 1

$a)\; \; A=\left(\begin{array}{cc}-4&3\\-7&10\end{array}\right)\\\\\\detA=-4\cdot 10+7\cdot 3=-19\\\\A_{11}=10\; \; \; ,\; \; \; A_{12}=7\; \; \; ,\; \; \; A_{21}=-3\; \; \; ,\; \; \; A_{22}=-4\\\\\\A^{-1}=-\frac{1}{19}\left(\begin{array}{cc}10&-3\\7&-4\end{array}\right)=\left(\begin{array}{cc}-\frac{10}{19}&\frac{3}{19}\\-\frac{7}{19}&\frac{4}{19}\end{array}\right)\\\\\\A\cdot A^{-1}=\left(\begin{array}{cc}-4&3\\-7&10\end{array}\right)\cdot \left(\begin{array}{cc}-\frac{10}{19}&\frac{3}{19}\\-\frac{7}{19}&\frac{4}{19}\end{array}\right)=\left(\begin{array}{cc}1&0\\0&1\end{array}\right)=E$

$A=\left(\begin{array}{ccc}3&7&10\\7&-4&3\\2&1&2\end{array}\right)\\\\\\detA=3(-8-3)-7(14-6)+10(7+8)=61\ne 0\\\\\\A_{11}=-11\; \; ,\; \; \; A_{12}=-8\; \; ,\; \; \; A_{13}=15\\\\A_{21}=-4\; \; ,\; \; \; A_{22}=-14\; \; ,\; \; A_{23}=11\\\\A_{31}=61\; \; ,\; \; A_{32}=61\; \; ,\; \; A_{33}=-61$

$A^{-1}=\frac{1}{61}\cdot \left(\begin{array}{ccc}-11&-4&61\\-8&-14&61\\15&11&-61\end{array}\right)\\\\\\A\cdot A^{-1}=\frac{1}{61}\cdot \left(\begin{array}{ccc}3&7&10\\7&-4&3\\2&1&2\end{array}\right)\cdot \left(\begin{array}{ccc}-11&-4&61\\-8&-14&61\\15&11&-61\end{array}\right)=\\\\\\=\left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right)=E$