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If A-B^(T)={:[(-2,2,1),(3,6,5)]:}andA^(T...

If `A-B^(T)={:[(-2,2,1),(3,6,5)]:}andA^(T)+B={:[(-4,5),(8,-2),(9,1)]:}`, then matrix A = _______ .

A

`{:[(3,-5,-5),(6,2,3)]:}`

B

`{:[(2,6,5),(3,5,7)]:}`

C

`{:[(9,5,7),(3,2,1)]:}`

D

`{:[(-3,5,5),(4,2,3)]:}`

Text Solution

Verified by Experts

The correct Answer is:
D
`A-B^(T)={:[(-2,2,1),(3,6,5)]:}`
`(A-B^(T))^(T)={:[(-2,3),(2,6),(1,5)]:}`
`A^(T)-B={:[(-2,3),(2,6),(1,5)]:}` (1)
`andA^(T)+B={:[(-4,5),(8,-9),(9,1)]:}` (2)
Add Eqs. (1) and (2),
`A^(T)-B+A^(T)+B={:[(-2,3),(2,6),(1,5)]:}+{:[(-4,5),(8,-2),(9,1)]:}`
`2A^(T)={:[(-6,8),(10,4),(10,6)]:}`
`A^(T)={:[(-3,4),(5,2),(5,3)]:}`
`A={:[(-3,5,5),(4,2,3)]:}`
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