If $\begin{bmatrix} x + y & 2x + z \\ x - y & 2z + w \end{bmatrix} = \begin{bmatrix} 4 & 7 \\ 0 & 10 \end{bmatrix}$,then the values of $x, y, z, w$ are

If $A = \begin{bmatrix} \alpha - 1 \\ 0 \\ 0 \end{bmatrix}$ and $B = \begin{bmatrix} \alpha + 1 \\ 0 \\ 0 \end{bmatrix}$ are two matrices,then $AB^T$ is a non-zero matrix for $|\alpha|$ not equal to:

Show that $\left[ {\begin{array}{cc} 5 & -1 \\ 6 & 7 \end{array}} \right] \left[ {\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}} \right] \ne \left[ {\begin{array}{cc} 2 & 1 \\ 3 & 4 \end{array}} \right] \left[ {\begin{array}{cc} 5 & -1 \\ 6 & 7 \end{array}} \right]$

Assume $X, Y, Z, W$ and $P$ are matrices of order $2 \times n, 3 \times k, 2 \times p, n \times 3$ and $p \times k$ respectively. If $n=p,$ then the order of the matrix $7X - 5Z$ is

Find the value of $x, y$ and $z$ from the following equation : $\begin{bmatrix} 4 & 3 \\ x & 5 \end{bmatrix} = \begin{bmatrix} y & z \\ 1 & 5 \end{bmatrix}$

Let $A = \begin{bmatrix} 2 & 4 \\ 3 & 2 \end{bmatrix}$,$B = \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}$,and $C = \begin{bmatrix} -2 & 5 \\ 3 & 4 \end{bmatrix}$. Find $BA$.