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If A = [(1,0,0),(0,1,1),(0,-2,4)] and a...

If `A = [(1,0,0),(0,1,1),(0,-2,4)] ` and also `A^(-1)=1/6 (A^(2)+cA+dI)` , where I is unit matrix , then the ordered pair (c,d) is :

A

`(6, 11)`

B

`(6, -11)`

C

`(-6, 11)`

D

`(-6,-11)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `A= [[1,0,0],[0,1,1],[0,-2,4]], A^(-1) = 1/6 [[6,0,0],[0,4,-1],[0,2,1]]`
`A^(2)= [[1,0,0],[0,1,1],[0,-2,4]] [[1,0,0],[0,1,1],[0,-2,4]]= [[1,0,0],[0,-1,5],[0,-10,14]]`
`cA= [[c,0,0],[0,c,c],[0,-2c,4c]] ,dI= [[d,0,0],[0,d,0],[0,0,d]]`
`therefore` By `A^(-1)=1/6[A^(2) + cA+dI]`
`rArr 6= 1 + c+d` [By equality of matrices]
`therefore (-6,11)` satisfy the relation.
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