JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Consider the system of linear equations \(x+y+z=5, x+2 y+\lambda^2 z=9\) \(x+3 y+\lambda z=\mu\), where \(\lambda, \mu \in R\). Then, which of the following statement is NOT correct?
- A System has infinite number of solution if \(\lambda=1\) and \(\mu=13\)
- B System is inconsistent if \(\lambda=1\) and \(\mu \neq 13\)
- C System is consistent if \(\lambda \neq 1\) and \(\mu=13\)
- D System has unique solution if \(\lambda \neq 1\) and \(\mu \neq 13\)
Answer & Solution
Correct Answer
(D) System has unique solution if \(\lambda \neq 1\) and \(\mu \neq 13\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left|\begin{array}{ccc}1 & 1 & 1 \\ 1 & 2 & \lambda^2 \\ 1 & 3 & \lambda\end{array}\right|=0 \\ & \Rightarrow 2 \lambda^2-\lambda-1=0 \\ & \lambda=1,-\frac{1}{2} \\ & \left|\begin{array}{ccc}1 & 1 & 5 \\ 2 & \lambda^2 & 9 \\ 3 & \lambda &…
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