CUET Mathematics 2022 17 Aug Shift 2 PYQs

If a matrix $A = \begin{bmatrix} 5 & -8 \\ -3 & 5 \end{bmatrix}$ then which of the following is / are TRUE?

(A) $|A| = 1$

(B) $A$ is a singular matrix.

(C) $-2A = \begin{bmatrix} 10 & -16 \\ -6 & 10 \end{bmatrix}$

(D) $AI = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}$ $I$ is an identity matrix of order 2.

Choose the correct answer from the options given below:

If $\mathrm{A}=\left[\begin{array}{ll}2 & 4 \\ 4 & 3\end{array}\right], \mathrm{X}=\left[\begin{array}{l}\mathrm{n} \\ 1\end{array}\right], \mathrm{B}=\left[\begin{array}{c}8 \\ 11\end{array}\right]$ and $A X=B$, then the value of $n$ will be :

The following system of equations:

$x + y - z = 7$

$4x + \lambda y - \lambda z = 3$

$3x + 2y - 4z = 5$

does not possess a solution if the value of $\lambda$ is: