Home
Class 12
MATHS
If A = [(5a,-b),(3,2)] and A adj A=AA^T...

If `A = [(5a,-b),(3,2)]` and `A adj A`=`A``A^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`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise JEE Advanced Previous Year|26 Videos

  • MATRICES

    CENGAGE|Exercise Single correct Answer|34 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Numerical)|24 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Single Correct Answer Type|46 Videos

Similar Questions

Explore conceptually related problems

If A=|{:(,5a,-b),(,3,2):}| and A adj A=A A^(T) , then 5a+b is equal to

If A=[[a,-b],[3,2]] and AadjA=A(A^(T)) then (5a+b)/(2)=

If A[(-1,5),(-3,2)] , then adj A=

If a*b=2a-3b+ab , then 3*5+5*3 is equal to:

If ( 3a+ 5b)/(3a- 5b) = 5 , then a: b is equal to

If a:b=5:7 , then (5a-3b):(4a-2b) is equal to :

If A=[(a,b),(c,d)] , then adj(adjA) is equal to