CUET · MATHS · PYQ PAPER 2023
Evaluate the determinant \(\begin{vmatrix} x-y & y-z & z-x \\ y-z & z-x & x-y \\ z-x & x-y & y-z \end{vmatrix}\)
- A x + y + z
- B 3xyz
- C (x - y)(y - z)(z - x)
- D \(0\)
Answer & Solution
Correct Answer
(D) \(0\)
Step-by-step Solution
Detailed explanation
Apply \(R_1 \to R_1 + R_2 + R_3\) \(R_1 = (x-y)+(y-z)+(z-x), (y-z)+(z-x)+(x-y), (z-x)+(x-y)+(y-z)\) \(R_1 = 0, 0, 0\) Since one row is all zeros, the determinant is \(0\).
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