JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]\) If \(A^3=4 A^2-A-21 I\), where I is the identity matrix of order \(3 \times 3\), then \(2 a+3 b\) is equal to :
- A \(-10\)
- B \(-13\)
- C \(-9\)
- D \(-12\)
Answer & Solution
Correct Answer
(B) \(-13\)
Step-by-step Solution
Detailed explanation
\( A^3-4 A^2+A+21 I=0 \) \( \operatorname{tr}(A)=4=5+6 \Rightarrow b=-1 \) \( |A|=-21 \) \( -16+a=-21 \Rightarrow a=-5 \) \( 2 a+3 b=-13\)
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