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If A=[(-1,3),(2,1)] then 1+A+A^(2)+…………....

If `A=[(-1,3),(2,1)]` then `1+A+A^(2)+…………..+oo` is equal to

A

`-1/6[(0,3),(2,2)]`

B

`1/6[(0,3),(2,2)]`

C

`-[(0,3),(2,2)]`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Now, in a given series `l+A+A^(2)+…………..oo` first terma `a=l` and common ratio `r=A`
`:.` The sum of infinite GP series `=a/(l-r)=l/(l-A)` ltrgt `=l(l-A)^(-1)implies(l-A)^(-1)`
`=([(1,0),(0,1)]-[(-1,3),(2,1)])^(-1)`
`=[(2,-3),(-2,0)]^(-1)`
: `=1/(|A|)adjA=1/(0-6)[(0,3),(2,2)]`
`=1/(-6)[(0,3),(2,2)]`
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