Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Basis and Dimension
Basis and Dimension Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
|
556 videos|198 docs
|
FAQs on Basis and Dimension Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is the definition of basis in linear algebra? |  |
Ans. In linear algebra, the basis of a vector space is a set of vectors that are linearly independent and span the entire vector space. It means that any vector in the vector space can be expressed as a unique linear combination of the basis vectors.
| 2. How is the dimension of a vector space related to its basis? | |
Ans. The dimension of a vector space is equal to the number of vectors in any basis for that vector space. In other words, all bases of the same vector space will have the same number of vectors, and this number is called the dimension of the vector space.
| 3. Can a vector space have multiple bases? | |
Ans. Yes, a vector space can have multiple bases. In fact, any vector space with dimension greater than zero will have infinitely many different bases. However, all these bases will have the same number of vectors, which is equal to the dimension of the vector space.
| 4. What is the significance of basis and dimension in solving systems of linear equations? | |
Ans. The basis and dimension of a vector space play a crucial role in solving systems of linear equations. The dimension determines the number of variables in the system, while the basis provides a set of vectors that can be used to express any solution to the system. By finding the basis and dimension, we can identify the number of independent equations needed to find a unique solution to the system.
| 5. Can the basis of a vector space be empty? | |
Ans. No, the basis of a vector space cannot be empty. It must contain at least one vector. An empty set of vectors cannot span any vector space, and therefore cannot form a basis. The dimension of a vector space is always a positive integer, indicating the minimum number of vectors required to form a basis.
Related Exams
About this Video
|
Nov 22, 2024 Last updated |
Video Description: Basis and Dimension for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Basis and Dimension have been prepared according to the Mathematics exam syllabus.
Information about Basis and Dimension covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Basis and Dimension.
Introduction of Basis and Dimension in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Basis and Dimension in
Hindi for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET 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 Basis and Dimension Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for IIT JAM, GATE, CSIR NET, UGC NET.
Information about Basis and Dimension
Here you can find the meaning of Basis and Dimension defined & explained in the simplest way possible.
Besides explaining types of Basis and Dimension theory, EduRev gives you an ample number of questions to practice Basis and Dimension tests,
examples and also practice Mathematics tests.
|
556 videos|198 docs
|
|
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
practice quizzes
,Sample Paper
,Important questions
,UGC NET
,Summary
,Basis and Dimension Video Lecture | Mathematics for IIT JAM
,Basis and Dimension Video Lecture | Mathematics for IIT JAM
,video lectures
,GATE
,UGC NET
,past year papers
,Free
,ppt
,Semester Notes
,UGC NET
,study material
,Previous Year Questions with Solutions
,MCQs
,CSIR NET
,shortcuts and tricks
,CSIR NET
,Extra Questions
,GATE
,mock tests for examination
,CSIR NET
,GATE
,Exam
,Objective type Questions
,Basis and Dimension Video Lecture | Mathematics for IIT JAM
,Viva Questions
,
Study Basis and Dimension on the App
Students of Mathematics can study Basis and Dimension alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Basis and Dimension,
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 Basis and Dimension 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