Find the value of x + y from the following equation : 2 $\left(\begin{array}{l l }x & 5 \\ 7 & y-3\end{array}\right)$ + $\left(\begin{array}{l l }3 & -4 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }7 & 6 \\ 15 & 14\end{array}\right)$ .

Simplify : cosθ $\left(\begin{array}{l l }cosθ & sinθ \\ -sinθ & cosθ\end{array}\right)$ + sinθ $\left(\begin{array}{l l }sinθ & -cosθ \\ cosθ & sinθ\end{array}\right)$

If matrix A = $\left(\begin{array}{l l }3 & -3 \\ -3 & 3\end{array}\right)$ and A² = λA, then write the value of λ.

If $\left(\begin{array}{l l }2 & 3 \\ 5 & 7\end{array}\right)$ $\left(\begin{array}{l l }1 & -3 \\ -2 & 4\end{array}\right)$ = $\left(\begin{array}{l l }-4 & 6 \\ -9 & x\end{array}\right)$ , write the value of x.

If matrix A = $\left(\begin{array}{l l }1 & -1 \\ -1 & 1\end{array}\right)$ and A² = kA, then write the value of k.

If matrix A = $\left(\begin{array}{l l }2 & -2 \\ -2 & 2\end{array}\right)$ and A² = pA, then write the value of p.

If $\left(\begin{array}{l l }2x & 3\end{array}\right)$ $\left(\begin{array}{l l }1 & 2 \\ -3 & 0\end{array}\right)$ $\left(\begin{array}{l }x \\ 3\end{array}\right)$ = 0,

If A = $\left(\begin{array}{l l }cosα & sinα \\ -sinα & cosα\end{array}\right)$ , find α satisfying $0\leq\alpha\leq{\frac{\pi}{4}}$ when $A+A^{T}=\sqrt{2}I$ where $A^{T}$ is transpose of A.

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

If $\left(\begin{array}{l l l }2 & 1 & 3\end{array}\right)$ $\left(\begin{array}{l l l }-1 & 0 & -1 \\ -1 & 1 & 0 \\ 0 & 1 & 1\end{array}\right)$ $\left(\begin{array}{l }1 \\ 0 \\ -1\end{array}\right)$ = A , then write the order of matrix A.

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

Write the order of product matrix $\left(\begin{array}{l }1 \\ 2 \\ 3\end{array}\right)$ $\left(\begin{array}{l l l }2 & 3 & 4\end{array}\right)$

If a matrix has 5 elements, then write all possible orders it can have.

For a 2 x 2 matrix, A = [$a_{i j}$] whose elements are given by $a_{i j}$ = $i/j,$ write the value of $a_{12}\,.$

If A = $\left(\begin{array}{l l }x & x-y \\ 2x+y & 7\end{array}\right)$ = $\left(\begin{array}{l l }3 & 1 \\ 8 & 7\end{array}\right)$ , then find the value of y.