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) → \(x=\displaystyle\frac{1}{2},y=6\)
Two matrices are equal when their corresponding elements are equal:
\( \displaystyle 2x - 1 = 0, \text{ so } x = \frac{1}{2} \)
\(4 = y - 2\), so \(y = 6\)
The other two elements agree with these values:
\(y - 1 = 6 - 1 = 5\)
\(3 + 2x = 3 + 1 = 4\)
So \(x = \frac{1}{2}\) and \(y = 6\).