Найти обратную матрицу. Created by Jackoe89. algebra-ru

Найти обратную матрицу...

Ulkiorik

Ответ:

$A=\left(\begin{array}{ccc}0&-6&-2\\-4&-2&1\\-1&-1&-2\end{array}\right)\\\\\\detA=6\cdot (8+1)-2\cdot (4-2)=54-4=50\\\\A_{11}=4+1=5\ \ \ ,\ \ \ \ A_{12}=-(8+1)=-9\ \ ,\ \ \ \ \ \ A_{13}=4-2=2\\\\A_{21}=-(12-2)=-10\ \ ,\ \ A_{22}=0-2=-2\ \ ,\ \ \ A_{23}=-(0-6)=6\\\\A_{31}=-6-4=-10\ \ ,\ \ \ A_{32}=-(0-8)=8\ \ ,\ \ \ A_{33}=0-24=-24\\\\\\A^{-1}=\dfrac{1}{50}\cdot \left(\begin{array}{ccc}5&-10&-10\\-9&-2&8\\2&6&-24\end{array}\right)$ Проверка:

$A^1\cdot A=\dfrac{1}{50}\cdot \left(\begin{array}{ccc}5&-10&-10\\-9&-2&8\\2&6&-24\end{array}\right)\cdot \left(\begin{array}{ccc}0&-6&-2\\-4&-2&1\\-1&-1&-2\end{array}\right)=\\\\\\=\dfrac{1}{50}\cdot \left(\begin{array}{ccc}50&0&0\\0&50&0\\0&0&50\end{array}\right)=\left(\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right)=E$

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