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Let P = 1 0 0 3 1 0 9 3 1 and Q = q i j be two 3 × 3 matrices such that Q - P 5 = I 3 . Then q 21 + q 31 q 32 is equal to :

Options

  1. A10
  2. B9
  3. C15
  4. D135

Correct answer

A. 10

Step-by-step solution

Given, P = 1 0 0 3 1 0 9 3 1 ⇒ P 2 = 1 0 0 3 1 0 9 3 1 1 0 0 3 1 0 9 3 1 = 1 0 0 6 1 0 27 6 1 ⇒ P 4 = P 2 × P 2 = 1 0 0 6 1 0 27 6 1 1 0 0 6 1 0 27 6 1 = 1 0 0 12 1 0 90 12 1 ⇒ P 5 = P 4 × P = 1 0 0 12 1 0 90 12 1 1 0 0 3 1 0 9 3 1 = 1 0 0 15 1 0 135 15 1 Let, Q = q 11 q 12 q 13 q 21 q 22 q 23 q 31 q 31 q 33 Now, given Q - P 5 = I 3 ⇒ q 21 - 15 = 0 ,   q 31 - 135 = 0 ,    q 32 - 15 = 0 ⇒ q 21 = 15 ,   q 31 = 135 ,   q 32 = 15 ∴ q 21 + q 31

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