Question

What is \[\operatorname{adj}A\] for \[A=\begin{bmatrix}1&1&1\\0&1&3\\1&-2&1\end{bmatrix}\]?

Options

• \[\begin{bmatrix}7&-3&2\\3&0&-3\\1&3&1\end{bmatrix}\]

• \[\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}\]

• \[\begin{bmatrix}7&3&-1\\-3&0&3\\2&-3&1\end{bmatrix}\]

• \[\begin{bmatrix}1&1&1\\0&1&3\\1&-2&1\end{bmatrix}\]

Answer 1

The adjoint is obtained by transposing the cofactor matrix. For this matrix, it is \[\operatorname{adj}A=\begin{bmatrix}7&-3&2\\3&0&-3\\-1&3&1\end{bmatrix}.\]