JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
The number of values of \(\alpha\) for which the system of equations: \(x+y+z=\alpha\) ; \(\alpha x+2 \alpha y+3 z=-1\) ; \(x+3 \alpha y+5 z=4\) is inconsistent, is
- A \(0\)
- B \(1\)
- C \(2\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(x+y+z=\alpha\) \(\alpha x+2 \alpha y+3 z=-1\) \(x+3 \alpha y+5 z=4\) Has inconsistent solution \(D =\left|\begin{array}{ccc}1 & 1 & 1 \\ \alpha & 2 \alpha & 3 \\ 1 & 3 \alpha & 5\end{array}\right|=0\) \(\Rightarrow(\alpha-1)^{2}=0\) \(\alpha=1\) For \(\alpha=1\)…
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