Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Properties of Vector Space
Properties of Vector Space Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Properties of Vector Space Video Lecture - Mathematics for Competitive Exams
| 1. What are the properties of a vector space in mathematics? |  |
Ans. The properties of a vector space in mathematics include closure under addition and scalar multiplication, associativity and commutativity of addition, existence of an additive identity and additive inverses, distributivity of scalar multiplication with respect to addition, and compatibility of scalar multiplication with field multiplication.
| 2. How do you prove closure under addition in a vector space? | |
Ans. To prove closure under addition in a vector space, we need to show that if two vectors are in the vector space, their sum is also in the vector space. This can be done by demonstrating that the sum of two vectors satisfies all the properties of a vector space, such as associativity, commutativity, and existence of an additive identity and additive inverses.
| 3. What does it mean for a vector space to be commutative? | |
Ans. In the context of vector spaces, commutativity refers to the property that the order of vector addition does not matter. In other words, if u and v are vectors in a vector space, then u + v = v + u. This property allows us to freely rearrange vectors when performing addition operations.
| 4. How is distributivity of scalar multiplication related to vector spaces? | |
Ans. Distributivity of scalar multiplication is one of the properties that a vector space must satisfy. It states that for any scalar c and vectors u and v in the vector space, c(u + v) = cu + cv. This property ensures that scalar multiplication distributes over vector addition, allowing us to perform scalar multiplication on vectors in a consistent manner.
| 5. What is the significance of the existence of an additive identity in a vector space? | |
Ans. The existence of an additive identity in a vector space is a fundamental property. It states that there exists a vector 0 such that for any vector u in the vector space, u + 0 = u. This property ensures that every vector in the space has an element that acts as a neutral element under vector addition. It also guarantees that the vector space is non-empty and that there is a starting point for vector addition operations.
Related Exams
About this Video
|
4.75/5 Rating |
|
Nov 22, 2024 Last updated |
Video Description: Properties of Vector Space for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Properties of Vector Space have been prepared according to the Mathematics exam syllabus.
Information about Properties of Vector Space covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Properties of Vector Space.
Introduction of Properties of Vector Space in English is available as part of our Mathematics for Competitive Exams for Mathematics & Properties of Vector Space in
Hindi for Mathematics for Competitive Exams course. Download more important topics related with notes, lectures and mock test series for
Mathematics Exam by signing up for free.
Description
Video Lecture & Questions for Properties of Vector Space Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Properties of Vector Space
Here you can find the meaning of Properties of Vector Space defined & explained in the simplest way possible.
Besides explaining types of Properties of Vector Space theory, EduRev gives you an ample number of questions to practice Properties of Vector Space tests,
examples and also practice Mathematics tests.
|
98 videos|27 docs|30 tests
|
|
Explore Courses for Mathematics exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Viva Questions
,Extra Questions
,Properties of Vector Space Video Lecture | Mathematics for Competitive Exams
,past year papers
,practice quizzes
,video lectures
,shortcuts and tricks
,Sample Paper
,Exam
,Important questions
,Previous Year Questions with Solutions
,Free
,MCQs
,ppt
,Properties of Vector Space Video Lecture | Mathematics for Competitive Exams
,Semester Notes
,Summary
,study material
,Objective type Questions
,Properties of Vector Space Video Lecture | Mathematics for Competitive Exams
,mock tests for examination
;
Study Properties of Vector Space on the App
Students of Mathematics can study Properties of Vector Space alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Properties of Vector Space,
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 Properties of Vector Space is prepared as per the latest Mathematics syllabus.
|
© 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