Q.If [5 3; x 7] = [y 3; 7 x], then (x+y) is equal to

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: $5=y \Rightarrow y=5$.

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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 $A=B$.

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