List of top Mathematics Questions on Matrices asked in Karnataka PGCET

If $A = \begin{pmatrix} \alpha & 2 \\ 2 & \alpha \end{pmatrix}$ and $|A^3| = 125$, then what is the value of $\alpha$?

If $ A = \begin{bmatrix} 1 & 2 \\ -1 & 3 \end{bmatrix} $, $ B = \begin{bmatrix} -1 & 2 \\ 0 & 4 \end{bmatrix} $, then match the following and choose the correct answer.

\[ \begin{array}{ll} \text{List - I} & \text{List - II} \\ \\ (a)\; A+B & (i)\; \begin{bmatrix} -1 & 10 \\ 1 & 10 \end{bmatrix} \\ (b)\; A-B & (ii)\; \begin{bmatrix} 0 & 4 \\ -1 & 7 \end{bmatrix} \\ (c)\; AB & (iii)\; \begin{bmatrix} 1 & 4 \\ 0 & 10 \end{bmatrix} \\ (d)\; 2A + B' & (iv)\; \begin{bmatrix} 2 & 0 \\ -1 & -1 \end{bmatrix} \end{array} \]

If $A = \begin{bmatrix} 1 & 2 & 4 \\ -1 & 3 & 0 \\ 1 & 2 & 0 \end{bmatrix}$, then the value of determinant of A is:}

If $ A = \begin{bmatrix} \cos \theta & \sin \theta & 0 \\ \sin \theta & -\cos \theta & 0 \\ 0 & 0 & 1 \end{bmatrix} $, then the value of $ AA' $ is:

The inverse of a symmetric matrix is a:

If \[ \begin{bmatrix} x + y + z \\ x + y \\ y + z \end{bmatrix} = \begin{bmatrix} 9 \\ 5 \\ 7 \end{bmatrix} \] then the value of $(x, y, z)$ is: