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If A = [(5a,-b),(3,2)] and A adj A=AA^T...

If `A = [(5a,-b),(3,2)]` and `A adj A=AA^T` , then `5a+b` is equal to:

A

5

B

4

C

13

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
A
A adj `A=A A^(T)`
`implies |A|I=A A^(T)`
`implies (10a+3b) [(1,0),(0,1)]=[(5a,-b),(3,2)][(5a,3),(-b,2)]`
`implies 25a^(2)+b^(2)=10a+3b, 15a-2b=0, 10a+3b=13`
`implies 10a+(3.15a)/2=13`
`implies 65a=2xx13`
`implies a=2/5`
`implies 5a=2`
`implies 2b=6`
`implies b=3`
`:. 5a+b=5`
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