JEE Exam > JEE Videos > Mathematics (Maths) Class 12 > Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices)
Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture | Mathematics (Maths) Class 12 - JEE
|
204 videos|290 docs|139 tests
|
FAQs on Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. Why is matrix multiplication non-commutative? |  |
Ans. Matrix multiplication is non-commutative because the order in which matrices are multiplied affects the result. In other words, if we have matrices A and B, multiplying A with B gives a different result than multiplying B with A. This is different from ordinary multiplication of numbers, where the order does not matter.
| 2. Can you provide an example to illustrate the non-commutativity of matrix multiplication? | |
Ans. Certainly! Let's consider two matrices A and B.
Matrix A: [1 2] Matrix B: [3 4]
[5 6] [7 8]
If we multiply A with B, we get:
A * B = [1*3 + 2*7 1*4 + 2*8]
[5*3 + 6*7 5*4 + 6*8]
= [17 20]
[51 60]
On the other hand, if we multiply B with A, we get:
B * A = [3*1 + 4*5 3*2 + 4*6]
[7*1 + 8*5 7*2 + 8*6]
= [23 34]
[39 58]
As you can see, A * B is not equal to B * A, thus illustrating the non-commutativity of matrix multiplication.
| 3. What are the implications of matrix multiplication being non-commutative? | |
Ans. The non-commutativity of matrix multiplication has significant implications in various fields such as physics, computer graphics, and cryptography. It means that the order in which operations are performed can greatly impact the final result. For example, in physics, the order of transformations applied to objects can affect their final position. In computer graphics, the order of transformations can alter the appearance of rendered objects. In cryptography, the non-commutativity of matrices is utilized in encryption algorithms to enhance security.
| 4. Are there any special cases where matrix multiplication is commutative? | |
Ans. Yes, there are special cases where matrix multiplication can be commutative. One such case is when the matrices being multiplied are scalar multiples of each other. In this case, the order of multiplication does not matter, and the result will be the same. For example, if matrix A is a scalar multiple of matrix B, i.e., A = k * B, where k is a scalar, then A * B = B * A.
| 5. How can we determine if two given matrices will result in a commutative multiplication? | |
Ans. To determine if two given matrices will result in a commutative multiplication, we can multiply the matrices in both orders and compare the results. If the two products are equal, then the multiplication is commutative. However, if the products are not equal, then the multiplication is non-commutative. This method allows us to verify the commutativity of matrix multiplication for specific cases.
Related Exams
About this Video
|
4.97/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) have been prepared according to the JEE exam syllabus.
Information about Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) covers all important topics for JEE 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices).
Introduction of Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) in English is available as part of our Mathematics (Maths) Class 12 for JEE & Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) in
Hindi for Mathematics (Maths) Class 12 course. Download more important topics related with notes, lectures and mock test series for
JEE Exam by signing up for free.
Description
Video Lecture & Questions for Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture | Mathematics (Maths) Class 12 - JEE - JEE full syllabus preparation | Free video for JEE exam to prepare for Mathematics (Maths) Class 12.
Information about Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices)
Here you can find the meaning of Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) defined & explained in the simplest way possible.
Besides explaining types of Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) theory, EduRev gives you an ample number of questions to practice Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) tests,
examples and also practice JEE tests.
|
204 videos|290 docs|139 tests
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Exam
,Important questions
,MCQs
,practice quizzes
,Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture | Mathematics (Maths) Class 12 - JEE
,Summary
,shortcuts and tricks
,Extra Questions
,mock tests for examination
,Free
,Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture | Mathematics (Maths) Class 12 - JEE
,video lectures
,Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) Video Lecture | Mathematics (Maths) Class 12 - JEE
,Semester Notes
,Viva Questions
,ppt
,past year papers
,Previous Year Questions with Solutions
,Sample Paper
,Objective type Questions
,study material
;
Study Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) on the App
Students of JEE can study Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices),
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of Multiplication of Matrices : Part 3 (Non Commutativity of Multiplication of Matrices) is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup