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 $\begin{bmatrix}0&y-2\\5&4\end{bmatrix}$
Answer & explanation
Correct answer: option 2
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: $x = \frac12,\; y = 6$