JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Consider the following system of questions \(\alpha x+2 y+z=1\) ; \(2 \alpha x+3 y+z=1\) ; \(3 x+\alpha y+2 z=\beta\) . For some \(\alpha, \beta \in R\). Then which of the following is NOT correct.
- A It has no solution if \(\alpha=-1\) and \(\beta \neq 2\)
- B It has no solution for \(\alpha=-1\) and for all \(\beta \in R\)
- C It has no solution for \(\alpha=3\) and for all \(\beta \neq 2\)
- D It has a solution for all \(\alpha \neq-1\) and \(\beta=2\)
Answer & Solution
Correct Answer
(B) It has no solution for \(\alpha=-1\) and for all \(\beta \in R\)
Step-by-step Solution
Detailed explanation
\(D=\left|\begin{array}{ccc}\alpha & 2 & 1 \\ 2 \alpha & 3 & 1 \\ 3 & \alpha & 2\end{array}\right|=0 \Rightarrow \alpha=-1,3\) \(D_x=\left|\begin{array}{lll}2 & 1 & 1 \\ 3 & 1 & 1 \\ \alpha & 2 & \beta\end{array}\right|=0 \Rightarrow \beta=2\)…
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