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If A = [ (1,2,2),(2,1,-2),(a,2,b)] is ...

If `A = [ (1,2,2),(2,1,-2),(a,2,b)] ` is a matrix satifying the equation `"AA"^(T)= 9I ` where I is a `3xx3` identify matrix , thenthe ordered pair (a,b) is equal to :

A

(2, 1)

B

(-2, -1)

C

`(2, -1)`

D

`(-2, 1)`

Text Solution

Verified by Experts

The correct Answer is:
B
`therefore A A^(T) = 9 I`
`[[1,2,2],[2,1,-2],[a,2,b]][[1,2,a],[2,1,2],[2,-2,b]]= 9 [[1,0,0],[0,1,0],[0,0,1]]`
`rArr [[9,0,a+ 4+ 2b],[0,9,2a+2-2b],[a+4+2b,2a+2-2b,a^(2)+4+b^(2)]]= [[9,0,0],[0,9,0],[0,0,9]]`
On comparing, we get
`a + 2b + 4 = 0 " " (i)`
` 2a- 2b+2=0" "(ii)`
From Eqs. (i) and (ii), we get
`a = -2,`
`b= -1`
`therefore` Prdered pair is `(-2, -1)`.
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