MatricesHard
Question
If P is a 3 × 3 matrix such that PT = 2P + I, where PT is the transpose of P and I is the 3 × 3 identity matrix, then there exists a column matrix X = 
such that
such thatOptions
A.PX = 
B.PX = X
C.PX = 2X
D.PX = - X
Solution
Give PT = 2P + I
⇒ P = 2PT + I = 2(2P + I) + I
⇒ P + I = 0
⇒ PX + X = 0
PX = - X.
⇒ P = 2PT + I = 2(2P + I) + I
⇒ P + I = 0
⇒ PX + X = 0
PX = - X.
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