JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\lambda \in R .\) The system of linear equations \(2 x_{1}-4 x_{2}+\lambda x_{3}=1\) \(x_{1}-6 x_{2}+x_{3}=2\) \(\lambda x_{1}-10 x_{2}+4 x_{3}=3\) is inconsistent for
- A exactly one negative value of \(\lambda\).
- B exactly one positive value of \(\lambda\).
- C every value of \(\lambda\).
- D exactly two values of \(\lambda\).
Answer & Solution
Correct Answer
(A) exactly one negative value of \(\lambda\).
Step-by-step Solution
Detailed explanation
\(D=\left|\begin{array}{ccc}2 & -4 & \lambda \\ 1 & -6 & 1 \\ \lambda & -10 & 4\end{array}\right|\) \(=2(3 \lambda+2)(\lambda-3)\) \(D_{1}=-2(\lambda-3)\) \(D _{2}=-2(\lambda+1)(\lambda-3)\) \(D_{3}=-2(\lambda-3)\) When \(\overline{\lambda=3}\), then…
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