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Question

# Let P=⎡⎢⎣1416014001⎤⎥⎦ and I be the identity matrix of order 3. If Q=[qij] is a matrix such that P50−Q=I, then q31+q32q21 equals

A
52
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B
103
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C
201
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D
205
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Solution

## The correct option is A 103P=⎡⎢⎣1004101641⎤⎥⎦⇒P2=⎡⎢⎣10081016(1+2)81⎤⎥⎦,P3=⎡⎢⎣100121016(1+2+3)121⎤⎥⎦P50=⎡⎢⎣1004×501016(1+2+..50)4×501⎤⎥⎦,P50=⎡⎢⎣10020010 204002001⎤⎥⎦∵P50−Q=I⇒⎡⎢⎣10020010204002001⎤⎥⎦−⎡⎢⎣q11q12q13q21q22q23q31q32q33⎤⎥⎦=⎡⎢⎣100001001⎤⎥⎦⇒200−q21=0⟹q21=200⇒20400−q31=0⇒q31=20400 and 200−q32=0⇒q32=200∴q31+q32q21=20400+200200=103

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