Home
Class 12
MATHS
If A={:[(1,4,2),(-1,2,3)]:}andB={:[(1,0,...

If `A={:[(1,4,2),(-1,2,3)]:}andB={:[(1,0,0),(0,-1,1)]:}`, verify that
(i) `(A^('))^(')=A`
(ii) `(kB)^(')=kB^(')`
(iii) `(A+B)^(')=A^(')+B^(')`

Text Solution

Verified by Experts

(i) Given `A{:[(1,4,2),(-1,2,3)]:},B={:[(1,0,0),(0,-1,1)]:}`
Now, `A^(')={:[(1,-1),(4,2),(2,3)]:},B^(')={:[(1,0),(0,-1),(0,1)]:}`
`(A^('))^(')={:[(1,-1),(4,2),(2,3)]:}={:[(1,4,2),(-1,2,3)]:}=A`
(ii) `kB={:[(k,0,0),(0,-k,k)]:}`
`(kB)^(')={:[(k,0),(0,-k),(0,k)]:}=k{:[(1,0),(0,-1),(0,1)]:}=*B^(')`
(iii) Now, `A+B={:[(1,4,2),(-1,2,3)]:}+{:[(1,0,0),(0,-1,1)]:}`
`={:[(2,4,2),(-1,1,4)]:}`
`(A+B)^(')={:[(2,-1),(4,1),(2,4)]:}`
Now, `A^(')+B^(')={:[(1,-1),(4,2),(2,3)]:}+{:[(1,0),(0,-1),(0,1)]:}={:[(2,-1),(4,1),(2,4)]:}=(A+B)^(')`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH INSTITUTE|Exercise Example 17|1 Videos

  • MATRICES

    AAKASH INSTITUTE|Exercise Example 18|1 Videos

  • MATRICES

    AAKASH INSTITUTE|Exercise Example 15|1 Videos

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos

  • PERMUTATIONS AND COMBINATIONS

    AAKASH INSTITUTE|Exercise Assignment Section-J (Aakash Challengers Questions)|7 Videos

Similar Questions

Explore conceptually related problems

If A=[{:(0,-1,2),(4,3,-4):}] and B=[{:(4,0),(1,3),(2,6):}] then verify that (i) (A')'=A (ii) (AB)'=B'A'

If A={:[(0,-1),(1,0)]:}andB={:[(-1,0),(3,2)]:} , then AB^(2) =

if A'=[{:(3,4),(-1,2),(0,1):}]and B=[{:(-1,2,1),(1,2,3):}], then verify that (i) (A+B)'=A'+B'(ii) (A-B)'=A'-B'

If A={:[(1,2,3),(3,2,1)]:},B={:[(1,-1,4),(2,3,1)]:} , verify that (i) (B')'=B , (ii) (a-B)'=A'-B' (iii) (A+B)'=A'+B' , (iv) (kA)'=kA', where k is any constant (v) (2A+3B)'=2A'+3B'

A={:[(1,2,3),(4,1,-1),(2,3,1)]:},B={:[(1,-1,1),(2,0,1),(1,1,1)]:} , verify (AB)'=B'A'.

If A'=[(3,4),(-1,2),(0,1)] and B=[(-1,2,1),(1,2,3)] , then verify that (A+B)'=A'+B'

Let A={:[(1,2,3),(0,1,0)]:}andB={:[(-1,4,3),(1,0,0)]:} Find 2A +3B.

If A=[{:(" "2,-3,5),(-1," "0,3):}]" and "B=[{:(3,2,-2),(4,-3," "1):}] , verify that (A+B)=(B+A).

If A=[(5,-1),(6,7)],B=[(2,1),(3,4)] and C=[(1,3),(-1,4)] , verify the following : (i) (A')'=A (ii) (A+B)'=A'+B' (iii) (3A)'=3A' (iv) (AB)'=B'A' .

If A=[(-1,1,0),(0,-1,1),(2,3,4)] verify that 3/4A'=(3/4A)^'