JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A = \begin{bmatrix} \alpha & 1 & 2 \\ 2 & 3 & 0 \\ 0 & 4 & 5 \end{bmatrix}\) and \(B = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -5\alpha & 0 \\ 0 & 4\alpha & -2\alpha \end{bmatrix} + \text{adj}(A)\). If \(\det(B)=66\), then \(\det(\text{adj}(A))\) equals:
- A \(289\)
- B \(361\)
- C \(441\)
- D \(529\)
Answer & Solution
Correct Answer
(C) \(441\)
Step-by-step Solution
Detailed explanation
The cofactor matrix of \(A\) is calculated as follows: \(C_{11} = 15\), \(C_{12} = -10\), \(C_{13} = 8\) \(C_{21} = 3\), \(C_{22} = 5\alpha\), \(C_{23} = -4\alpha\) \(C_{31} = -6\), \(C_{32} = 4\), \(C_{33} = 3\alpha - 2\) The adjoint of \(A\) is the transpose of the cofactor…
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