Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Vector Subspace: Subspace Theorems & Examples
Vector Subspace: Subspace Theorems & Examples Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Vector Subspace: Subspace Theorems & Examples Video Lecture - Mathematics for Competitive Exams
| 1. What are vector subspaces? |  |
Ans. Vector subspaces are subsets of a vector space that satisfy three conditions: closure under addition (if u and v are in the subspace, then u+v is also in the subspace), closure under scalar multiplication (if u is in the subspace and c is a scalar, then cu is also in the subspace), and containing the zero vector (the subspace must contain the zero vector).
| 2. What are some examples of vector subspaces? | |
Ans. Examples of vector subspaces include the set of all solutions to a homogeneous linear system (also known as the null space or kernel), the span of a set of vectors, and the column space and row space of a matrix.
| 3. What are the subspace theorems related to vector subspaces? | |
Ans. The subspace theorems state that if a subset of a vector space satisfies the closure properties (closure under addition and scalar multiplication) and contains the zero vector, it is a subspace. Additionally, any intersection of subspaces is also a subspace, and the union of subspaces may or may not be a subspace.
| 4. How can vector subspaces be visualized? | |
Ans. Vector subspaces can be visualized as planes, lines, or even just the origin in three-dimensional space. In two-dimensional space, subspaces can be visualized as lines or the origin. The dimension of a subspace corresponds to the number of linearly independent vectors needed to span it.
| 5. What is the significance of vector subspaces in mathematics? | |
Ans. Vector subspaces play a fundamental role in linear algebra and various areas of mathematics. They allow for the study of linear transformations, eigenvectors, and eigenvalues, as well as providing a framework for solving systems of linear equations and understanding the properties of matrices.
Related Exams
About this Video
|
4.78/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Vector Subspace: Subspace Theorems & Examples for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Vector Subspace: Subspace Theorems & Examples have been prepared according to the Mathematics exam syllabus.
Information about Vector Subspace: Subspace Theorems & Examples covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Vector Subspace: Subspace Theorems & Examples.
Introduction of Vector Subspace: Subspace Theorems & Examples in English is available as part of our Mathematics for Competitive Exams for Mathematics & Vector Subspace: Subspace Theorems & Examples 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 Vector Subspace: Subspace Theorems & Examples Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Vector Subspace: Subspace Theorems & Examples
Here you can find the meaning of Vector Subspace: Subspace Theorems & Examples defined & explained in the simplest way possible.
Besides explaining types of Vector Subspace: Subspace Theorems & Examples theory, EduRev gives you an ample number of questions to practice Vector Subspace: Subspace Theorems & Examples 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
shortcuts and tricks
,mock tests for examination
,Viva Questions
,Exam
,Vector Subspace: Subspace Theorems & Examples Video Lecture | Mathematics for Competitive Exams
,video lectures
,Sample Paper
,Vector Subspace: Subspace Theorems & Examples Video Lecture | Mathematics for Competitive Exams
,MCQs
,past year papers
,study material
,Objective type Questions
,Vector Subspace: Subspace Theorems & Examples Video Lecture | Mathematics for Competitive Exams
,Free
,ppt
,Important questions
,practice quizzes
,Semester Notes
,Previous Year Questions with Solutions
,Summary
,Extra Questions
;
Study Vector Subspace: Subspace Theorems & Examples on the App
Students of Mathematics can study Vector Subspace: Subspace Theorems & Examples alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Vector Subspace: Subspace Theorems & Examples,
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 Vector Subspace: Subspace Theorems & Examples is prepared as per the latest Mathematics 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