Mathematics Exam > Mathematics Videos > Mathematics for IIT JAM, GATE, CSIR NET, UGC NET > Linear Dependence & Independence
Linear Dependence & Independence Video Lecture | Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
|
556 videos|198 docs
|
FAQs on Linear Dependence & Independence Video Lecture - Mathematics for IIT JAM, GATE, CSIR NET, UGC NET
| 1. What is linear dependence and independence? |  |
Ans. Linear dependence refers to a situation where a vector can be expressed as a linear combination of other vectors in a given set. On the other hand, linear independence occurs when no vector in a set can be written as a linear combination of the others in that set.
| 2. How can we determine if a set of vectors is linearly dependent or independent? | |
Ans. To determine the linear dependence or independence of a set of vectors, we can consider the following condition: If the only solution to the equation c1v1 + c2v2 + ... + cnvn = 0 (where c1, c2, ..., cn are constants and v1, v2, ..., vn are the vectors in the set) is c1 = c2 = ... = cn = 0, then the set is linearly independent. Otherwise, it is linearly dependent.
| 3. Can a set of vectors be both linearly dependent and independent? | |
Ans. No, a set of vectors cannot be both linearly dependent and independent at the same time. It is either one or the other. If a set is linearly dependent, it means that at least one vector in the set can be expressed as a linear combination of the others. Conversely, if a set is linearly independent, no vector in the set can be written as a linear combination of the others.
| 4. Is the zero vector always included in a linearly dependent set of vectors? | |
Ans. Yes, the zero vector (0) is always included in a linearly dependent set of vectors. This is because the zero vector can always be expressed as a linear combination of any other vectors in the set by assigning all the scalar coefficients to be zero.
| 5. Can a set of two vectors be linearly dependent if one vector is a scalar multiple of the other? | |
Ans. Yes, a set of two vectors can be linearly dependent if one vector is a scalar multiple of the other. In such a case, one vector can be expressed as a scalar multiple of the other, indicating a linear dependence. For example, if v1 = 2v2, then the set {v1, v2} is linearly dependent.
Related Exams
About this Video
|
Nov 24, 2024 Last updated |
Video Description: Linear Dependence & Independence for Mathematics 2024 is part of Mathematics for IIT JAM, GATE, CSIR NET, UGC NET preparation.
The notes and questions for Linear Dependence & Independence have been prepared according to the Mathematics exam syllabus.
Information about Linear Dependence & Independence covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Linear Dependence & Independence.
Introduction of Linear Dependence & Independence in English is available as part of our Mathematics for IIT JAM, GATE, CSIR NET, UGC NET for Mathematics & Linear Dependence & Independence 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 Linear Dependence & Independence 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 Linear Dependence & Independence
Here you can find the meaning of Linear Dependence & Independence defined & explained in the simplest way possible.
Besides explaining types of Linear Dependence & Independence theory, EduRev gives you an ample number of questions to practice Linear Dependence & Independence 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
UGC NET
,Exam
,Previous Year Questions with Solutions
,Free
,Linear Dependence & Independence Video Lecture | Mathematics for IIT JAM
,Summary
,Objective type Questions
,shortcuts and tricks
,Important questions
,CSIR NET
,MCQs
,CSIR NET
,CSIR NET
,Sample Paper
,ppt
,Extra Questions
,Viva Questions
,mock tests for examination
,Linear Dependence & Independence Video Lecture | Mathematics for IIT JAM
,GATE
,practice quizzes
,past year papers
,GATE
,Linear Dependence & Independence Video Lecture | Mathematics for IIT JAM
,video lectures
,GATE
,Semester Notes
,UGC NET
,study material
,UGC NET
;
Study Linear Dependence & Independence on the App
Students of Mathematics can study Linear Dependence & Independence alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Linear Dependence & Independence,
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 Linear Dependence & Independence 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