If $\left[ {\begin{array}{*{20}{c}}{x + y}&{2x + z}\\{x – y}&{2z + w}\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}4&7\\0&{10}\end{array}} \right]$, then values of $x, y, z, w$ are

If $M = \left[ {\begin{array}{*{20}{c}}1&2\\2&3\end{array}} \right]$ and ${M^2} – \lambda M – {I_2} = 0$, then $\lambda = $

Suppose $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$ is a real matrix with non-zero entries, $\alpha d-b c=0$ and $A^2=A$. Then, $a + d$ equals

If $A = \left[ {\begin{array}{*{20}{c}}1&{\tan \theta /2}\\{ – \tan \theta /2}&1\end{array}} \right]$ and $AB = I$, then $B = $

If $A = \left[ {\begin{array}{*{20}{c}}
1&0\\
{\frac{1}{2}}&1
\end{array}} \right]$ , then $A^{50}$ is