CUET · MATHS · PYQ PAPER 2025
If the system of equations \(k x+y+z=0, x+k y-z=0, x-y+z=0\) has a non-zero solution, then the possible values of \(k\) are
- A \(1, 3\)
- B \(1,-3\)
- C \(2, 3\)
- D \(-1, 3\)
Answer & Solution
Correct Answer
(D) \(-1, 3\)
Step-by-step Solution
Detailed explanation
\( \begin{vmatrix} k & 1 & 1 \\ 1 & k & -1 \\ 1 & -1 & 1 \end{vmatrix} = 0 \) \( k(k \cdot 1 - (-1)(-1)) - 1(1 \cdot 1 - (-1) \cdot 1) + 1(1 \cdot (-1) - k \cdot 1) = 0 \) \( k(k-1) - 1(1+1) + 1(-1-k) = 0 \) \( k^2 - k - 2 - 1 - k = 0 \) \( k^2 - 2k - 3 = 0 \)…
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