JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The values of \(\lambda\) and \(\mu\) for which the system of linear equations \(x+y+z=2\) \(x+2 y+3 z=5\) \(x+3 y+\lambda z=\mu\) has infinitely many solutions are, respectively
- A \(5\) and \(7\)
- B \(6\) and \(8\)
- C \(4\) and \(9\)
- D \(5\) and \(8\)
Answer & Solution
Correct Answer
(D) \(5\) and \(8\)
Step-by-step Solution
Detailed explanation
For infinite many solutions \(D=D_{1}=D_{2}=D_{3}=0\) \(\operatorname{Now} D =\left|\begin{array}{lll}1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & \lambda\end{array}\right|=0\) \(1 .(2 \lambda-9)-1 .(\lambda-3)+1 .(3-2)=0\) \(\therefore \lambda=5\)…
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