CUET · MATHS · PYQ PAPER 2023
If the matrix \(\left[\begin{array}{ccc}x-y & 1 & -2 \\ 2 x-y & 0 & 3 \\ 2 & -3 & 0\end{array}\right]\) is skew-symmetric, then the values of \(x\) and \(y\) are respectively:
- A \(\frac{1}{2}, 1\)
- B \(1, \frac{1}{2}\)
- C 1,1
- D \(-1,-1\)
Answer & Solution
Correct Answer
(D) \(-1,-1\)
Step-by-step Solution
Detailed explanation
A matrix \(A\) is skew-symmetric if \(A^T = -A\), meaning \(a_{ij} = -a_{ji}\) for all \(i, j\). From \(a_{11}=0\): \(x-y = 0\) From \(a_{12} = -a_{21}\): \(1 = -(2x-y) \Rightarrow 2x-y = -1\) Substitute \(y=x\) from the first equation into the second: \(2x-x = -1\) \(x = -1\)…
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