JEE Exam > JEE Questions > If A and B are symmetric matrices of same ord...
Start Learning for Free
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this?
Most Upvoted Answer
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-B...
Solution:
Given,
A and B are symmetric matrices of same order
X=AB BA and Y=AB-BA
To find: (XY)T
Approach:
We know that (AB)T = BTAT and (BA)T = ATBT
Using this property, we can find the transpose of X.
Then, we can find the transpose of XY by using the property (XY)T = YTX
Steps:
1. Transpose of X:
(X)T = (AB-BA)T
= (AB)T - (BA)T
= BTA - ATB
(using property (AB)T = BTAT and (BA)T = ATBT)
2. XY:
XY = (AB-BA)(AB+BA)
= ABBAB - ABBBA - BABA + BABBA
= ABBAB - ABBBA - BABA + ABABB
= A(BB-BA)B - B(AB-BA)A
= A(B-B)AB - B(A-A)BA
= 0
3. Transpose of XY:
(XY)T = 0T = 0
4. Comparison:
Comparing (XY)T with options,
A) XY ≠ (XY)T
B) XY ≠ (XY)T
C) -YX = (XY)T
Therefore, the answer is C.
Given,
A and B are symmetric matrices of same order
X=AB BA and Y=AB-BA
To find: (XY)T
Approach:
We know that (AB)T = BTAT and (BA)T = ATBT
Using this property, we can find the transpose of X.
Then, we can find the transpose of XY by using the property (XY)T = YTX
Steps:
1. Transpose of X:
(X)T = (AB-BA)T
= (AB)T - (BA)T
= BTA - ATB
(using property (AB)T = BTAT and (BA)T = ATBT)
2. XY:
XY = (AB-BA)(AB+BA)
= ABBAB - ABBBA - BABA + BABBA
= ABBAB - ABBBA - BABA + ABABB
= A(BB-BA)B - B(AB-BA)A
= A(B-B)AB - B(A-A)BA
= 0
3. Transpose of XY:
(XY)T = 0T = 0
4. Comparison:
Comparing (XY)T with options,
A) XY ≠ (XY)T
B) XY ≠ (XY)T
C) -YX = (XY)T
Therefore, the answer is C.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this?
Question Description
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this?.
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this?.
Solutions for If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? defined & explained in the simplest way possible. Besides giving the explanation of
If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this?, a detailed solution for If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? has been provided alongside types of If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? theory, EduRev gives you an
ample number of questions to practice If A and B are symmetric matrices of same order and X=AB BA and Y=AB-BA, then transpose of XY is equal to : A) XY b) YX C) -YX Answer is C. Can you explain this? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup