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Let P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[...

Let `P=[(1, 0, 0),(3, 1, 0),(9, 3, 1)]Q=[q_(ij)]` and `Q=P^5+I_3` then `(q_21+q_31)/q_32` is equal to (A) `12` (B) `8` (C) `10` (D) `20`

A

10

B

9

C

135

D

15

Text Solution

Verified by Experts

The correct Answer is:
A
`p^2=[(1,0,0),(3,1,0),(9,3,1)][(1,0,0),(3,1,0),(9,3,1)]=[(1,0,0),(6,1,0),(27,6,1)]`
`p^3=[(1,0,0),(6,1,0),(27,6,1)][(1,0,0),(3,1,0),(9,3,1)]=[(1,0,0),(9,1,0),(54,9,1)]`
Similarly, `p^5=[(1,0,0),(15,1,0),(135,15,1)]`
`Q=[(1,0,0),(15,1,0),(135,15,1)]+[(1,0,0),(0,1,0),(0,0,1)]=[(2,0,0),(15,2,0),(135,15,2)]`
`(q_21+q_31)/(q_32)=(15+135)/(15)=(150)/(15)=10` .
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