JEE Main 2024 Mathematics question
Let . If A³ = 4A² − A − 21I, where I is the identity matrix of order 3 × 3, then 2a + 3b is equal to:
Answer: (B)
Solution
A³ − 4A² + A + 21I = 0 says t³ − 4t² + t + 21 is the characteristic polynomial of A. The characteristic polynomial of A is t³ − (5 + b)t² +
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