PUC Science 2nd PUC Class 12 - Karnataka Board PUC Question Bank Solutions for Mathematics

If \[A = \begin{bmatrix}1 & - 2 & 3 \\ 0 & - 1 & 4 \\ - 2 & 2 & 1\end{bmatrix},\text{ find }\left( A^T \right)^{- 1} .\]

Find the adjoint of the matrix \[A = \begin{bmatrix}- 1 & - 2 & - 2 \\ 2 & 1 & - 2 \\ 2 & - 2 & 1\end{bmatrix}\]  and hence show that \[A\left( adj A \right) = \left| A \right| I_3\]. 

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}7 & 1 \\ 4 & - 3\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}5 & 2 \\ 2 & 1\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}1 & 6 \\ - 3 & 5\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}3 & 10 \\ 2 & 7\end{bmatrix}\]

Find the inverse by using elementary row transformations:

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

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}2 & 0 & - 1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}2 & 3 & 1 \\ 2 & 4 & 1 \\ 3 & 7 & 2\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}3 & - 3 & 4 \\ 2 & - 3 & 4 \\ 0 & - 1 & 1\end{bmatrix}\]

Find the inverse by using elementary row transformations:

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

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}2 & - 1 & 3 \\ 1 & 2 & 4 \\ 3 & 1 & 1\end{bmatrix}\]

Find the inverse by using elementary row transformations:

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

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}2 & - 1 & 4 \\ 4 & 0 & 7 \\ 3 & - 2 & 7\end{bmatrix}\]

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}3 & 0 & - 1 \\ 2 & 3 & 0 \\ 0 & 4 & 1\end{bmatrix}\]    

Find the inverse by using elementary row transformations:

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

Find the inverse by using elementary row transformations:

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

If adj \[A = \begin{bmatrix}2 & 3 \\ 4 & - 1\end{bmatrix}\text{ and adj }B = \begin{bmatrix}1 & - 2 \\ - 3 & 1\end{bmatrix}\]