Question

Нужно найти обратную матрицу

Answer 1

$mathcal4=-4+9-6=-1\A_{11}=(-1)^2* left[begin{array}{cc}4&0\1&1end{array}right] =4\A_{12}=(-1)^3* left[begin{array}{cc}3&0\0&1end{array}right]=-3\A_{13}=(-1)^4* left[begin{array}{cc}3&4\0&1end{array}right]=3\A_{21}=(-1)^3* left[begin{array}{cc}2&3\1&1end{array}right]=1\A_{22}=(-1)^4* left[begin{array}{cc}-1&3\0&1end{array}right]=-1\A_{23}=(-1)^5* left[begin{array}{cc}-1&2\0&1end{array}right]=1\A_{31}=(-1)^4* left[begin{array}{cc}2&3\4&0end{array}right]=-12$
$A_{32}=(-1)^5* left[begin{array}{cc}-1&3\3&0end{array}right]=9\A_{33}=(-1)^6* left[begin{array}{cc}-1&2\3&4end{array}right]=-10\A^T= left[begin{array}{ccc}A_{11}&A_{21}&A_{31}\A_{12}&A_{22}&A_{32}\A_{13}&A_{23}&A_{33}end{array}right]=left[begin{array}{ccc}4&1&-12\-3&-1&9\3&1&-10end{array}right]\A^{-1}=frac{1}{mathcal4}A^T=-1*left[begin{array}{ccc}4&1&-12\-3&-1&9\3&1&-10end{array}right]$