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Let P be an m m matrix such that P²=P . Then (1+P)^ n equals -

Options

  1. AI+P
  2. BI+n P
  3. CI+2^ n P
  4. DI+ (2^ n -1 ) P

Correct answer

D. I+ (2^ n -1 ) P

Step-by-step solution

array l P ²= P P ⁻¹ P ²= P ⁻¹ P P = I ( I + P )^ n =(2 P )^ n =2^ n P ^ n array =2^ n P = P + (2^ n -1 ) P = I + (2^ n -1 ) P

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