AP EAMCET · Maths · Matrices
If \(\alpha, \beta, \gamma(\alpha \lt \beta \lt \gamma)\) are the values of \(x\) such that \(\left[\begin{array}{ccc}x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2 x-1\end{array}\right]\) is a singular matrix then \(2 \alpha+3 \beta+4 \gamma=\)
- A \(4\)
- B \(0\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad\left|\begin{array}{ccc}x-2 & 0 & 1 \\ 1 & x+3 & 2 \\ 2 & 0 & 2 x-1\end{array}\right|=0 \\ & \Rightarrow(x-2)[(x+3)(2 x-1)]-2(x+3)=0 \\ & \Rightarrow x(x+3)(2 x-5)=0 \therefore x=0,-3, \frac{5}{2} \\ & \text { So, } \alpha=-3, \beta=0, \gamma=\frac{5}{2}…
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