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

Let `A={:[(-3,1),(0,2)]:}B={:[(2,-1),(0,1)]:}` Then prove

Text Solution

Verified by Experts

`A={:[(-3(2)+1(0),-3(-1)+1(1)),((0)2+2(0),0(-1)+2(1))]:}={:[(-6,4),(0,2)]:}`
`BA={:[(2,-1),(0,1)]:}{:[(-3,1),(0,2)]:}`
`={:[(2(-3)+(-1)0,2(1)+(-1)2),(0(-3)+1(0),(0)1+1(2))]:}={:[(-6,0),(0,2)]:}`.

Topper's Solved these Questions

MATRICES
PEARSON IIT JEE FOUNDATION|Exercise TEST YOUR CONCEPTS VERY SHORT ANSWER TYPE QUESTIONS|1 Videos
MATRICES
PEARSON IIT JEE FOUNDATION|Exercise TEST YOUR CONCEPTS (VERY SHORT ANSWER TYPE QUESTIONS)|28 Videos
LOGARITHMS
PEARSON IIT JEE FOUNDATION|Exercise Level 3 MCQ|15 Videos
NUMBER SYSTEMS
PEARSON IIT JEE FOUNDATION|Exercise Level 3|15 Videos

Similar Questions

Explore conceptually related problems

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

(i) if A=[{:(1,0),(0,1):}],B=[{:(0,1),(1,0):}]and C=[{:(1,0),(0,1):}], then show that A^(2)=B^(2)=C^(2)=I_(2). (ii) if A=[{:(1,0),(1,1):}],B=[{:(2,0),(1,1):}]and C=[{:(-1,2),(3,1):}], then show that A(B+C)=AB+AC. (iii) if A=[{:(1,-1),(-1,1):}]and B=[{:(1,1),(1,1):}], then show that AB is a zero matrix.

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

Find AB and BA if exists from the following matrices A and B: (i) A=[{:(2,3,-1),(0,1,2):}]and B=[{:(2,-6),(-4,0):}] (ii) A=[{:(1,2,3),(0,1,-2),(-1,0,-1):}]and B=[{:(0,0,2),(2,0,0),(0,2,0):}] (iii) A=[{:(0,3,4),(2,1,-2),(1,-3,-1):}]and B=[{:(2,1,3),(-1,0,-2):}]

If A=[(0,1),(1,0)] and B=[(1,0),(0,-1)], prove that :

Let A=[{:(0,1,-2),(5,-1,-4):}],B=[{:(1,-3,-1),(0,-2," "5):}]" and "C=[{:(2,-5,1),(-4," "0,6):}]. Compute 5A-3B+4C.

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

If A=[{:(" "1,-1," "2),(" "3," "2," "0),(-2," "0," "1):}],B=[{:(3,1),(0,2),(-2,5):}]" and "C=[{:(2,1,-3),(3,0,-1):} then verify that (AB)C=A(BC).

Let A+B+C= [{:(,4,-1),(,0,1):}],4A+2B+C=[{:(,0,-1),(,-3,2):}]and 9A+3B+C=[{:(,0,2),(,2,1):}]"then find A"

Let A=[(1,2,3),(2,0,5),(0,2,1)] and B=[(0),(-3),(1)] . Which of the following is true ?

PEARSON IIT JEE FOUNDATION-MATRICES-LEVEL 3

Let A={:[(-3,1),(0,2)]:}B={:[(2,-1),(0,1)]:} Then prove
Text Solution
|
If A={:[(p,-1),(q,1)]:},B={:[(1,-1),(1,2)]:}and(A+B)^(2)=A^(2)+2AB+B^(...
Text Solution
|
If P={:[(2,-1),(-1,3)]:},Q={:[(1,-2),(-3,0)]:}andR={:[(-2,1),(2,-1)]:}...
Text Solution
|
If {:((a,3),(4,5)):}{:((3,-2),(b,8)):}={:((30,20),(52,a)):}, then find...
Text Solution
|
If P=[2" "2" "1],Q=[1" "2" "3],R={:[(1),(2),(3)]:},andS={:[(3),(2),(1...
Text Solution
|
If y={:((4,-2),(3,0)):}andf(y)=y^(2)-y-6, find f(y).
Text Solution
|
If the matrix A={:[(5,-3),(5,-3)]:}," then "A^(n+1) = .
Text Solution
|
If A(x)={:[(e^(x),e^(x)),(e^(-x),e^(-x))]:} then A(x) A(y)=
Text Solution
|
If A={:[(6,-7,1),(3,-2,1)]:}andB={:[(5,1,2),(-4,3,-5)]:} then find X s...
Text Solution
|
If {:[(2,4),(p,1)]:}{:[(-1,2),(3,1)]:}={:[(10,q),(-2,r)]:}, then pq= ...
Text Solution
|
If A={:[(-13,24),(-7,13)]:}, then A^(8) = .
Text Solution
|
If A+B={:[(8,-9),(3,5)]:}andA-B={:[(6,5),(1,7)]:}, the A= .
Text Solution
|
If A={:[(7,9),(3,8)]:}andB={:[(13),(18)]:} then find the matrix X such...
Text Solution
|
If A={:[(a,b),(2,-1)]:},B={:[(1,1),(4,-1)]and(A+B)^(2)=A^(2)+B^(2), th...
Text Solution
|
If A={:[(6,x),(7,-6)]:}andA^(2)=I, then x= .
Text Solution
|
If A-B={:[(18,1,-9),(11,12,2)]:}andA+3B={:[(26,1,3),(-13,-16,10)]:}, t...
Text Solution
|
If A={:[(1,4),(-2,5)]:}andB={:[(-6,-1),(-8,2)]:}, then AB + BA = .
Text Solution
|
If A={:[(2,1),(0,3)]:}andf(x)=x^(2)-4x+3, then find f(A).
Text Solution
|
If[5" "6]{:[(1,-3),(-1,x)]:}{:[(3),(4)]:}=[-15], then the value of x ...
Text Solution
|
If A={:[(1,-4),(3,2)]:}andB={:[(6,-1),(3,2)]:}, then find the matrix C...
Text Solution
|
If A-B^(T)={:[(-2,2,1),(3,6,5)]:}andA^(T)+B={:[(-4,5),(8,-2),(9,1)]:},...
Text Solution
|