JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\mathrm{a} \in \mathbf{R}\) and A be a matrix of order \(3 \times 3\) such that \(\operatorname{det}(A)=-4\) and \(A+I=\left[\begin{array}{lll}1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2\end{array}\right]\), where \(I\) is the identity matrix of order \(3 \times 3\).
If \(\operatorname{det}((a+1) \operatorname{adj}((a-1) A))\) is \(2^m 3^n, m, n \in\) \(\{0,1,2, \ldots .20\}\), then \(\mathrm{m}+\mathrm{n}\) is equal to :
- A 14
- B 17
- C 15
- D 16
Answer & Solution
Correct Answer
(D) 16
Step-by-step Solution
Detailed explanation
\(A = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} - I = \begin{bmatrix} 0 & a & 1 \\ 2 & 0 & 0 \\ a & 1 & 1 \end{bmatrix}\) \(\operatorname{det}(A) = 0(0-0) - a(2-0) + 1(2-0) = -2a+2\) \(-2a+2 = -4 \Rightarrow -2a = -6 \Rightarrow a=3\)…
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