Which of the given values of $x$ and $y$ make the following pair of matrices equal?

$\begin{bmatrix}2x-1&4\\y-1&3+2x\end{bmatrix}$ and $\begin{bmatrix}0&y-2\\5&4\end{bmatrix}$

$x=\frac{1}{2},y=6$

The correct answer is Option (2) → $x=\frac{1}{2},y=6$ **

Two matrices are equal only if all corresponding entries are equal.

Given matrices:

$\begin{bmatrix} 2x-1 & 4 \\ y-1 & 3+2x \end{bmatrix} = \begin{bmatrix} 0 & y-2 \\ 5 & 4 \end{bmatrix}$

Equate elements:

$2x - 1 = 0$

$4 = y - 2$

$y - 1 = 5$

$3 + 2x = 4$

Solve:

From $2x - 1 = 0$:

$2x = 1$

$x = \frac12$

Check with $3 + 2x = 4$:

$3 + 1 = 4$ (correct)

From $y - 1 = 5$:

$y = 6$

Final answer: $x = \frac12,\; y = 6$