InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let `P=[[1,0,0],[4,1,0],[16,4,1]]`and `I` be the identity matrix of order `3`. If `Q = [q_()ij ]` is a matrix, such that `P^(50)-Q=I`, then `(q_(31)+q_(32))/q_(21)` equalsA. 52B. 103C. 201D. 205 |
|
Answer» Correct Answer - B We have, `{:P=[(1,0,0),(4,1,0),(16,4,1)]:}`. `:. {:P^2=PP=[(1,0,0),(4,1,0),(16,4,1)][(1,0,0),(4,1,0),(16,4,1)]=[(1,0,0),(8,1,0),(16+32,8,1)]:}` `:. {:P^3=P^2P=[(1,0,0),(8,1,0),(16+32,8,1)][(1,0,0),(4,1,0),(16,4,1)]=[(1,0,0),(12,1,0),(16+32+48,12,1)]:}` By observing the symmetry, we obtain `{:P^50=[(1,0,0),(4xx50,1,0),(16+32+48+...50"terms",4xx50,1)]:}` `rArr{:P^50[(1,0,0),(200,1,0),((16xx50xx51)/2,200,1)]:}` `:.P^50-Q=I` `rArr{:Q=P^50-I[(0,0,0),(200,0,0),(20400,200,0)]:}` `rArr q_21=200,q_31=20400and q_32=200` `:. (q_31+q_32)/q_21=(20400+200)/200=20600/200=103` |
|