JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the determinant of a square matrix \(A\) of order \(m\) be \(m-n\), where \(m\) and \(n\) satisfy \(4 m+n=22\) and \(17 m +4 n =93\). If \(\operatorname{det}(n \operatorname{adj}(\operatorname{adj}( mA )))=\) \(3^{ a } 5^{ b } 6^{ c }\). then \(a + b + c\) is equal to:
- A \(96\)
- B \(101\)
- C \(109\)
- D \(84\)
Answer & Solution
Correct Answer
(A) \(96\)
Step-by-step Solution
Detailed explanation
\(| A |= m - n\) \(4 m + n =22\) \(17 m +4 n =93\) \(m =5, n =2\) \(| A |=3\) \(\mid 2 \operatorname{adj}(\operatorname{adj} 5 A ))\left.\left|=2^5\right| 5 A \right|^{16}\) \(=2^5 \cdot 5^{80}| A |^{16}\) \(=2^5 \cdot 5^{80} \cdot 3^{16}\) \(=3^{11} \cdot 5^{80} \cdot 6^5\)…
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