JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The system of linear equations \(\lambda x+2 y+2 z=5\) ; \(2 \lambda x+3 y+5 z=8\) ; \(4 x+\lambda y+6 z=10\) has
- A infinitely many solutions when \(\lambda=2\)
- B a unique solution when \(\lambda=-8\)
- C no solution when \(\lambda=8\)
- D no solution when \(\lambda=2\)
Answer & Solution
Correct Answer
(D) no solution when \(\lambda=2\)
Step-by-step Solution
Detailed explanation
\(D=\left|\begin{array}{ccc}{\lambda} & {3} & {2} \\ {2 \lambda} & {3} & {5} \\ {4} & {\lambda} & {6}\end{array}\right|=(\lambda+8)(2-\lambda)\) for \(\lambda=2 ; \mathrm{D}_{1} \neq 0\) Hence, no solution for \(\lambda=2\)
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