Let P = 1 0 0 4 1 0 16 4 1 and I be the identity matrix of order 3 . If Q = q i j is a matrix such that P 50…

Let P=1004101641 and I be the identity matrix of order 3. If Q=qij is a matrix such that P50-Q=I, then the value of q31+q32q21 is equal to
  1. 52
  2. 103
  3. 201
  4. 205

Solution

P=1004101641  ⇒P2=10081016+3281
So, P3=100121016+32+48121
Using symmetry, we can write
P50=1002001016.50.5122001
As, P 50 −Q=I⇒Q= P 50 −I=[ 0 0 0 200 0 0 16.50.51 2 200 0 ] ,
q31=16.50.512,  q32=200 and q21=200
∴ q31+q32q21=16.50.512.200+1=102+1=103

Asked in: JEE Advanced 2016 (Paper 2)

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