Q.If $\begin{bmatrix}x & 3x-y\\zx+z & 3y-w\end{bmatrix}=\begin{bmatrix}3 & 2\\4 & 7\end{bmatrix}$ then .......... (A) $x=3,y=7,z=1,w=14$ (B) $x=3,y=-5,z=-1,w=-4$ (C) $x=3,y=6,z=2,w=7$ (D) $x=-3,y=-7,z=-1,w=-14$

Matrices of the same order can be checked for equality ($A=B$ iff every corresponding entry matches), added ($A+B=[a_{ij}+b_{ij}]$, entry-by-entry, undefined for mismatched orders), subtracted ($A-B=A+(-B)$), and scaled by a number ($kA=[k\,a_{ij}]$, every entry multiplied by $k$). These operations obey familiar-looking laws — addition is commutative ($A+B=B+A$) and associative ($(A+B)+C=A+(B+C)$), the zero matrix is the additive identity, $-A$ is the additive inverse, and scalar multiplication distributes over both matrix sums and scalar sums. The most common use is solving a linear matrix equation for an unknown matrix $X$ (e.g. $3A-4B+5X=C$): treat $X$ exac …