If 2 $\left(\begin{array}{l l }1 & 3 \\ 0 & x\end{array}\right)$ + $\left(\begin{array}{l l }y & 0 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }5 & 6 \\ 1 & 8\end{array}\right)$ , write the value of (x + y).

Find the value of a if $\left(\begin{array}{l l }a-b & 2a+c \\ 2a-b & 3c+d\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 5 \\ 0 & 13\end{array}\right)$ .

If $\left(\begin{array}{l l }x-y & 2y \\ 2y+z & x+y\end{array}\right)$ = $\left(\begin{array}{l l }1 & 4 \\ 9 & 5\end{array}\right)$

Find the matrix A if $\left(\begin{array}{l l l }9 & -1 & 4 \\ -2 & 1 & 3\end{array}\right)$ = A + $\left(\begin{array}{l l l }1 & 2 & -1 \\ 0 & 4 & 9\end{array}\right)$

If A is a 3 × 3 matrix, whose elements are given by $a_{i j}={\frac{1}{3}}|-3i+j\,|$ , then write the value of $a_{23}$.

Write the value of x + y + z if $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ y \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ -1 \\ 0\end{array}\right)$.

For a 2 × 2 matrix A = [ $a_{i j}$ ], whose elements are given by $a_{i j}=\,{\frac{(i+2j)^{2}}{4}}$ , write the value of $a_{\mathrm{21}}$.

If 3A – B = $\left(\begin{array}{l l }5 & 0 \\ 1 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l }4 & 3 \\ 2 & 5\end{array}\right)$ , then find the matrix A.

If $\left(\begin{array}{l l }2x+1 & 2y \\ 0 & y²+1\end{array}\right)$ = $\left(\begin{array}{l l }x+3 & 10 \\ 0 & 26\end{array}\right)$ , write the value of (x + y).

If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.

If matrix A = $[a_{i j}]_{2\times2}$, where $a_{i j}$ = $\left\{\begin{array}{l}{{2,\ i\neq j}}\\ {{0,\ i=j^{\prime}}}\end{array}\right.$ , Write the matrix A.

If $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ -1 \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ 2 \\ 1\end{array}\right)$ , find x + y + z.

If $\left(\begin{array}{l l }1 & 0 \\ y & 5\end{array}\right)$ + 2 $\left(\begin{array}{l l }x & 0 \\ 1 & -2\end{array}\right)$ = , where I is a 2×2 unit matrix, find (x – y).

If x $\left(\begin{array}{l }2 \\ 3\end{array}\right)$ + y $\left(\begin{array}{l }-y \\ y\end{array}\right)$ = $\left(\begin{array}{l }10 \\ 5\end{array}\right)$ , write the value of x.

If A' = $\left(\begin{array}{l l }3 & 4 \\ -1 & 2 \\ 0 & 1\end{array}\right)$ and B = $\left(\begin{array}{l l l }-1 & 2 & 1 \\ 1 & 2 & 3\end{array}\right)$ then find A' – B'.