CUET · MATHS · PYQ PAPER 2025
The system of equations \(x+y-z=1,3 x+y-2 z=3, x-y+\lambda z=1\) has infinite number of solutions if \(\lambda\) is equal to
- A 0
- B 2
- C -5/3
- D any real number
Answer & Solution
Correct Answer
(A) 0
Step-by-step Solution
Detailed explanation
\( \begin{vmatrix} 1 & 1 & -1 \\ 3 & 1 & -2 \\ 1 & -1 & \lambda \end{vmatrix} = 0 \) \( 1(\lambda - 2) - 1(3\lambda + 2) - 1(-3 - 1) = 0 \) \( \lambda - 2 - 3\lambda - 2 + 4 = 0 \) \( -2\lambda = 0 \) \( \lambda = 0 \)
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