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If P = 3 2 1 2 - 1 2 3 2 , A = 1 1 0 1 and Q = P A P T , then P T Q 2015 P is :

Options

  1. A0 2015 0 0
  2. B2015 0 1 2015
  3. C1 2015 0 1
  4. D2015 1 0 2015

Correct answer

C. 1 2015 0 1

Step-by-step solution

P = 3 2 1 2 - 1 2 3 2       P T = 3 2 - 1 2 1 2 3 2 P P T = P T P = I Q 2015 = P A P T   P A P T ......( 2015 terms) = P A 2015   P T ... i ∴   P T   Q 2015   P = P T P   A 2015 P T P = A 2015 from.. i Given A = 1 1 0 1 ⇒ A 2 = 1 1 0 1     1 1 0 1 = 1 2 0 1 ⇒ A 3 = 1 2 0 1   1 1 0 1 = 1 3 0 1 ∴ A 2015 = 1 2015 0 1

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