CUET · MATHS · PYQ PAPER 2023
The value/s of \(\lambda\) for which the given system of equations will have infinitely many solutions \(x+y-6 z=0 ; \lambda x-y+2 z=0 ;-3 x+\lambda y+2 z=0\), is/are:
- A \(\lambda=0\)
- B \(\lambda=3\)
- C \(\lambda=-\frac{5}{3}\) or 1
- D \(\lambda=\frac{5}{3}\) or \(\lambda=-1\)
Answer & Solution
Correct Answer
(C) \(\lambda=-\frac{5}{3}\) or 1
Step-by-step Solution
Detailed explanation
For infinitely many solutions, \(\det(A) = 0\). \(\begin{vmatrix} 1 & 1 & -6 \\ \lambda & -1 & 2 \\ -3 & \lambda & 2 \end{vmatrix} = 1(-2-2\lambda) - 1(2\lambda+6) - 6(\lambda^2-3) = -6\lambda^2 - 4\lambda + 10\) \(-6\lambda^2 - 4\lambda + 10 = 0\)…
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