Question

Find inverse of the following: \[ A=\left[\begin{array}{ccc} 2 & 6 & 3 \\ 4 & -1 & 3 \\ 1 & 3 & 2 \end{array}\right] \]

Answer 1

A = \(\begin{bmatrix}2&6&3\\4&-1&3\\1&3&2\end{bmatrix}\)

|A| = -4 + 18 + 36 + 3 - 18 - 48 = -13

Adj(A) = \(\begin{bmatrix}-11&-3&21\\-5&-1&6\\13&0&-26\end{bmatrix}\)

∴ A^-1 = \(\frac{adj(A)}{|A|}\) = \(-\frac1{13}\begin{bmatrix}-11&-3&21\\-5&1&6\\13&0&-26\end{bmatrix}\)