AP EAMCET · Maths · Matrices
If \(A=\left[\begin{array}{lll}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{array}\right]\) and \(\operatorname{det}\left(A^3\right)=125\), then \(x=\)
- A \(1 / 3\)
- B \(3\)
- C \(-\frac{1}{3}\)
- D \(-3\)
Answer & Solution
Correct Answer
(A) \(1 / 3\)
Step-by-step Solution
Detailed explanation
\(|A|=\left|\begin{array}{lll}x & 2 & 1 \\ 2 & x & 1 \\ 2 & 1 & 0\end{array}\right|=x(0-1)-2(0-2)+1(2-2 x)\) \(=6-3 x\) According to question, \(\left|A^3\right|=125\) \(\Rightarrow \quad|A|^3=5^3 \quad\left[\because\left|A^3\right|=|A|^3\right]\)…
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