Find x from the matrix equation $\left(\begin{array}{l l }1 & 3 \\ 4 & 5\end{array}\right)$ $\left(\begin{array}{l }x \\ 2\end{array}\right)$ = $\left(\begin{array}{l }5 \\ 6\end{array}\right)$ .

If A = $\left(\begin{array}{l l }cosα & -sinα \\ sinα & cosα\end{array}\right)$ , then for what value of a, A is an identity matrix ?

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.

If A is a matrix of order 3 x 4 and B is a matrix of order 4 x 3, then find order of matrix (AB.)

If $\left(\begin{array}{l l }2x+y & 3y \\ 0 & 4\end{array}\right)$ = $\left(\begin{array}{l l }6 & 0 \\ 0 & 4\end{array}\right)$ then find the value of x.

If A = $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ then find A + A’.

If A = $\left(\begin{array}{l l }3 & 4 \\ 2 & 3\end{array}\right)$then find A + A’., where A’ is transpose of A.

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

If matrix A = [1 2 3], then write AA’.

If A = $\left(\begin{array}{l l }3 & 1 \\ -1 & 2\end{array}\right)$ and I = $\left(\begin{array}{l l }1 & 0 \\ 0 & 1\end{array}\right)$ find k so that A² = 5A + kI.

If A = $\left(\begin{array}{l l l }2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right)$ , find A² – 5A + 4I and hence find a matrix X such that A² – 5A + 4I + X = 0.

For the following matrices A and B, verify that [AB]’ = B’A’ where, A = $\left(\begin{array}{l }1 \\ -4 \\ 3\end{array}\right)$ , B = $\left(\begin{array}{l l l }-1 & 2 & 1\end{array}\right)$

If A = $\left(\begin{array}{l l }1 & -1 \\ 2 & -1\end{array}\right)$ , B = $\left(\begin{array}{l l }a & 1 \\ b & -1\end{array}\right)$ and (A + B)² = A²+ B², then find the values of a and b.

If A = $\left(\begin{array}{l l l }2 & 0 & 1 \\ 2 & 1 & 3 \\ 1 & -1 & 0\end{array}\right)$ , then find value of A² - 3A + 2I.

Three schools A, B and C organised a fete (mela) collecting funds for flood victims in which they sold hand-helds fans, mats and toys made from recycled material, the sale price of each being ₹ 25, ₹ 100 and ₹ 50 respectively. The following table shows the number of articles of each type sold :