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Let A= [ array lll 2 & a & 0 1 & 3 & 1 0 & 5 & b array ] . If A^3=4 A^2-A-21 I , where I is the identity matrix of order 3 3 , then 2 a+3 b is equal to

Options

  1. A-9
  2. B-13
  3. C-10
  4. D-12

Correct answer

B. -13

Step-by-step solution

aligned & A^3-4 A^2+A+21 I=0 & tr (A)=4=5+6 b=-1 & |A|=-21 & -16+a=-21 a=-5 & 2 a+3 b=-13 aligned

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