If $2\begin{bmatrix}3 & 4 \\ 5 & x\end{bmatrix} + \begin{bmatrix}1 & y \\ 0 & 1\end{bmatrix} = \begin{bmatrix}7 & 0 \\ 10 & 5\end{bmatrix}$, then the value of $x-y$ is :

If $A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}$, $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ and $A² = KA - 2I$, then the value of K is

If $[1 \quad 2 \quad 1] \begin{bmatrix} -1 & 0 & 1 \\ 1 & 2 & -1 \\ 0 & 1 & 3 \end{bmatrix} \begin{bmatrix} 2x \\ x \\ -7 \end{bmatrix} = [0]$, then the value of $x$ is

Let $A = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}$ and $I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$. If $A^T + A = I$, then

Let $A = [a_{ij}]$ be a $2 \times 2$ matrix such that $a_{ij} = \frac{|-3i+j|}{2}$ then $a_{21}$ is :

If $A=\begin{bmatrix}1 & 1 & 1\\1 & 0 & 3\\1 & -2 & 1\end{bmatrix}$, then

Match List-I with List-II

Choose the correct answer from the options given below:

The system of equations

$x - 3y - 8z = -10$

$2x + 5y + \lambda z = 13$

$3x + y - 4z = 0$

has infinite number of solutions if the value of $\lambda$ is equal to: