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If P is a 3 3 matrix such that P^ T =2 P+I , where P^ T is the transpose of P and I is the 3 3 identity matrix, then there exists a column matrix X= [ array l x y z array ] [ array l 0 0 0 array ] such that

Options

  1. AP X= [ array l 0 0 0 array ]
  2. BP X=X
  3. CP X=2 X
  4. DP X=-X

Correct answer

D. P X=-X

Step-by-step solution

P^ T =2 P+I array l P=2 P^ T +I P=2(2 P+I)+I P=4 P+3 I P+I=0 P X+X=0 P X=-X array

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