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

If `A=[(1,2,2),(2,1,-2),(a,2,b)]` is a matrix satisfying the equation `AA^T=""9I` , where `I` is `3xx3` identity matrix, then the 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:
D
`A A^(T)=9I`
`implies [(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)]`
`implies [(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)]`
`implies a+4+2b=0, 2a+2-2b=0, a^(2)+4+b^(2)=9`
`implies a=-2, b=-1`
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