KVPY SB SX Exam 2011 Question Paper

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Question : 3 of 120

Marks: +1, -0

Let P be an m × m matrix such that

P^2=P

. Then

(I+P)^n

equals

$I+P$
$I+nP$
$I+2^nP$
$I+(2^n-1)P$

Solution:

P^2 = P

P^{–1} P^2 = P^{–1} P

P = I

(I + P)^n = (2P)^n = 2^n P^n

= 2^nP

= P + (2^n - 1) P

= I + (2^n - 1) P

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