Question

Найдите матрицу, обратную к данной матрице Di

Answer 1

$D=\left(\begin{array}{ccc}-1&1&8\\2&-3&2\\0&-2&6\end{array}\right)\\\\\\detD=-(-18+4)-(12-0)+8(-4-0)=-30\ne 0\\\\A_{11}=-18+4=-14\ \ ,\ \ \ A_{12}=-(12-0)=-12\ \ ,\ \ \ A_{13}=-4-0=-4\\\\A_{21}=-(6+16)=-22\ \ ,\ \ \ A_{22}=-6-0=-6\ \ ,\ \ A_{23}=-(2-0)=-2\\\\A_{31}=2+24=26\ \ ,\ \ \ A_{32}=-(-2-16)=18\ \ ,\ \ A_{33}=3-2=1\\\\\\D^{-1}=-\cfrac{1}{30}\cdot \left(\begin{array}{ccc}-14&-22&26\\-12&-6&18\\-4&-2&1\end{array}\right)$