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If A=[(5a,-b),(3,2)] and A*adjA="A"A^T ...

If `A=[(5a,-b),(3,2)]` and `A*adjA="A"A^T` , then `5a+b` is equal to:
`(1)` `-1`
` (2)`. `5`
`(3). 4`
`(4). 13`

A

5

B

13

C

4

D

-1

Text Solution

Verified by Experts

The correct Answer is:
A
`because A" adj "A = A A^(T)`
`rArr A^(-1) (A" adj " A) = A^(-1) (A A^(T))`
`rArr (A^(-1)A)" adj " A = (A^(-1) A) A^(T)`
`rArr I ( " ADj " A ) = IA^(T)`
or ` " adj " A = A^(T)`
or `[[2,b],[-3,5a]]=[[5a,3],[-b,2]]`
`rArr 5 a = 2 and b = 3`
`therefore 5a + b = 5`
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