Home
Class 12
MATHS
If A=[(2,-1),(1,3)], then A^(-1)=?...

If `A=[(2,-1),(1,3)], then A^(-1)`=?

A

`[(3/7,(-1)/7),(1/7,2/7)]`

B

`[(3/7,(1)/7),((-1)/7,2/7)]`

C

`[(3/7,(1)/7),(1/7,2/7)]`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`|A|=|(2,-1),(1,3)|=(6+1)=7 ne 0`
`M_(11)=3,M_(12)=1,M_(21)=-1 and M_(22)=2`
`therefore C_(11)=3,C_(12)=-1,C_(21)=1 and C_(22)=2`
`rArr AdjA=[(3,-1),(1,2)]=[(3,1),(-1,2)]`
`rArr A^(-1)=1/(|A|)(adjA)=1/7[(3,1),(-1,2)]=[(3/7,1/7),(-1/7,2/7)]`
Promotional Banner

Topper's Solved these Questions

  • SYSTEM OF LINEAR EQUATIONS

    RS AGGARWAL|Exercise EXERCISE 8A (VALUE BASED QUESTIONS)|4 Videos

  • STRAIGHT LINE IN SPACE

    RS AGGARWAL|Exercise Objective Questions|19 Videos

  • THE PLANE

    RS AGGARWAL|Exercise Objective Questions|35 Videos

Similar Questions

Explore conceptually related problems

If A = [(2,2,1), (1,3,1), (1,2,2)] then A^-1+(A-5I) (AI)^2 = (i) 1/ 5 [[4,2, -1], [-1,3,1], [-1,2,4]] (ii) 1/5 [[4, -2, -1], [-1, 3, -1], [-1, -2,4]] (iii) 1/3 [[4,2, -1], [-1,3,1], [-1,2,4]] (iv) 1/3 [[4, -2, -1], [-1,3, -1], [-1, -2,4]]

Let A=[[2,1,3],[1,1,2],[3,1,1]] and A^(-1)=?

Find the value of [(1/2)^(-1) + (1/3)^(-1)]^(-1)

A={:[(1,2,1),(3,1,4)]:},B={:[(1,-1),(2,3),(-1,1)]:} , verify (AB)'=B'A'

Find the value of (1/2)^(-1)+(1/3)^(-1)+(1/4)^(-2)

Find the rank of A=[[-2,-1,-3,-1],[1,2,3,-1],[1,0,1,1],[0,1,1,-1]]

Find the values of - ((1)/(2))^(-1)+((1)/(3))^(-1)+((1)/(4))^(-1)

If S =(y-1-1/2(y-1)^(2)+1/3(y-1))^(3)/(a-1-1/2(a-1)^(2)+1/3(a-1)^(3) …. Then S is equal to