JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of real values \(\lambda\), such that the system of linear equations \(2 x-3 y+5 z=9\) ; \(x+3 y-z=-18\) ; \(3 x-y+\left(\lambda^{2}-1 \lambda \mid\right) z=16\) has no solution, is :-
- A \(0\)
- B \(1\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\Delta=\left|\begin{array}{ccc}2 & -3 & 5 \\ 1 & 3 & -1 \\ 3 & -1 & \lambda^{2}-|\lambda|\end{array}\right|=2\left(3 \lambda^{2}-3|\lambda|-1\right)\) \(+3\left(\lambda^{2}-|\lambda|+3\right)\) \(+5(-1-9)\) \(=9 \lambda^{2}-9|\lambda|-43\) \(=9|\lambda|^{2}-9|\lambda|-43\)…
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