JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be a \(3 \times 3\) matrix such that \(\operatorname{adj} A=\left[\begin{array}{ccc}2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1\end{array}\right]\) and \(B = adj (\) adj \(A )\) If \(| A |=\lambda\) and \(\left|\left( B ^{-1}\right)^{ T }\right|=\mu,\) then the ordered pair \((|\lambda|, \mu)\) is equal to
- A \(\left(9, \frac{1}{9}\right)\)
- B \(\left(9, \frac{1}{81}\right)\)
- C \(\left(3, \frac{1}{81}\right)\)
- D \((3,81)\)
Answer & Solution
Correct Answer
(C) \(\left(3, \frac{1}{81}\right)\)
Step-by-step Solution
Detailed explanation
\(C =\operatorname{adj} A =\left|\begin{array}{ccc}+2 & -1 & 1 \\ -1 & 0 & 2 \\ 1 & -2 & -1\end{array}\right|\) \(C |=| \operatorname{adj} A \mid=+2(0+4)+1 .(1-2)+1 .(2,4)\) \(=+8-1+2\) \(|\operatorname{adj} A|=|A|^{2}=9=9\) \(\lambda=|A|=\pm 3\) \(|\lambda|=3\) \(B = adj C\)…
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