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Question

# Let P=âŽ¡âŽ¢âŽ£1004101641âŽ¤âŽ¥âŽ¦ and I be the identity matrix of order 3. If Q=[qij] is a matrix, such that p50âˆ’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 B 103P=⎡⎢⎣1004101641⎤⎥⎦P2=⎡⎢⎣1004101641⎤⎥⎦⎡⎢⎣1004101641⎤⎥⎦=⎡⎢⎣1008104881⎤⎥⎦P3=⎡⎢⎣1008104881⎤⎥⎦⎡⎢⎣1004101641⎤⎥⎦=⎡⎢⎣100121056121⎤⎥⎦P4=⎡⎢⎣1008104881⎤⎥⎦⎡⎢⎣1004101641⎤⎥⎦=⎡⎢⎣1001610160161⎤⎥⎦∴P50=⎡⎢⎣1004×5010p314×501⎤⎥⎦Q=⎡⎢⎣q11q12q13q21q22q23q31q32q33⎤⎥⎦P50−Q=⎡⎢⎣100010001⎤⎥⎦⇒4×50−q21=0p31−q31=04×50−q32=qOn observing,p311=16×1p312=16×(1+2)p313=16×(1+2+3)p3150=16×(1+2+3+.....50)=16×50×512∴q31+q32q21=p31+p32p21=16×25×51+4×504×50=103

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