Question

Найти обратную матрицу
ДАЮ 50 БАЛОВ

Answer 1

Ответ:

$A=\left(\begin{array}{ccc}2&3&1\\4&-1&0\\0&1&2\end{array}\right)\\\\\\\Delta =\left|\begin{array}{ccc}2&3&1\\4&-1&0\\0&1&2\end{array}\right|=2(-2-0)-3(8-0)+1(4-0)=-24\ne 0\\\\\\A_{11}=-2\ \ \ ,\ \ \ A_{12}=-8\ \ \ ,\ \ \ A_{13}=4\\\\A_{21}=-5\ \ \ ,\ \ \ A_{22}=4\ \ \ ,\ \ \ A_{23}=-2\\\\A_{31}=1\ \ \ ,\ \ \ A_{32}=4\ \ \ ,\ \ \ A_{33}=-14$

$A^{-1}=-\dfrac{1}{24}\cdot \left(\begin{array}{ccc}-2&-5&1\\-8&4&4\\4&-2&-14\end{array}\right)=\left(\begin{array}{ccc}\frac{1}{12} &\frac{5}{24}&-\frac{1}{24}\\\frac{1}{3}&\frac{1}{6}&\frac{1}{6}\\\frac{1}{6}&\frac{1}{12}&\frac{7}{12}\end{array}\right)$