Q.Determine the value of $x+y$ if

[!FORMULA] $\begin{pmatrix} 2x+y & 4x \\ 5x-7 & 4x\end{pmatrix} = \begin{pmatrix} 7 & 7y-13 \\ y & x+6\end{pmatrix}$

Two matrices are equal only when every corresponding entry matches; compare entries one at a time.

Step 1. $\begin{bmatrix}5 & 3\\ x & 7\end{bmatrix} = \begin{bmatrix}y & 3\\ 7 & x\end{bmatrix}$.

Step 2. Comparing the $(1,1)$ entries: $5=y \Rightarrow y=5$.

Step 3. Comparing the $(2,1)$ entries: $x=7$. (Comparing $(2,2)$: $7=x$ — consistent.)

Step 4. $x+y = 7+5 = 12$.

Two matrices are equal iff every corresponding entry is equal — match the entries of $A$ and $B$ directly.

Given $A=\begin{pmatrix}a\\6\end{pmatrix}$ and $B=\begin{pmatrix}3\\b\end{pmatrix}$, with $A=B$.

Equating corresponding entries (two matrices of the same size are equal iff every entry matches):

Row 1: $a=3$

Row 2: $6=b$, i.e. $b=6$

So $(a,b) = (3,6)$, matching option (a).