JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], C=\mathrm{ABA}^{\mathrm{T}}\) and \(\mathrm{X}\) \(=\mathrm{A}^{\mathrm{T}} \mathrm{C}^2 \mathrm{~A}\), then \(\operatorname{det} \mathrm{X}\) is equal to :
- A \(243\)
- B \(729\)
- C \(27\)
- D \(891\)
Answer & Solution
Correct Answer
(B) \(729\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & A=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right] \Rightarrow \operatorname{det}(A)=3 \\ & B=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right] \Rightarrow \operatorname{det}(B)=1\end{aligned}\) Now…
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