Civil Engineering (CE) Exam > Civil Engineering (CE) Videos > Engineering Mathematics > Vector Space - Linear Algebra
Vector Space - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
|
65 videos|120 docs|94 tests
|
FAQs on Vector Space - Linear Algebra Video Lecture - Engineering Mathematics - Civil Engineering (CE)
| 1. What is a vector space in linear algebra? |  |
Ans. A vector space is a mathematical structure consisting of a set of vectors, along with operations of addition and scalar multiplication, that satisfy certain axioms. These axioms include closure under addition and scalar multiplication, associativity, commutativity, and the existence of an additive identity and additive inverses.
| 2. How are vector spaces useful in linear algebra? | |
Ans. Vector spaces are fundamental in linear algebra as they provide a framework for understanding and solving problems involving vectors and linear transformations. They allow us to perform operations such as addition, scalar multiplication, and linear combinations, which are essential in many applications, including physics, engineering, and computer science.
| 3. What are some examples of vector spaces? | |
Ans. Some common examples of vector spaces include the set of all n-dimensional real vectors, denoted as R^n, where n is a positive integer. Other examples include the set of polynomials of degree at most n, denoted as P^n, and the space of continuous functions on a given interval.
| 4. What are the properties of vector spaces? | |
Ans. Vector spaces have several key properties. These include closure under addition and scalar multiplication, associativity of addition and scalar multiplication, commutativity of addition, existence of an additive identity element (the zero vector), existence of additive inverses for each vector, and distributivity properties involving addition and scalar multiplication.
| 5. How do we determine if a set is a vector space? | |
Ans. To determine whether a set is a vector space, we need to verify that it satisfies all the axioms or properties of a vector space. This involves checking if the set is closed under addition and scalar multiplication, if the axioms of associativity, commutativity, and distributivity hold, and if the zero vector and additive inverses exist for each vector in the set.
Related Exams
About this Video
|
11.2K Views |
|
4.60/5 Rating |
|
Dec 03, 2024 Last updated |
Video Description: Vector Space - Linear Algebra for Civil Engineering (CE) 2024 is part of Engineering Mathematics preparation.
The notes and questions for Vector Space - Linear Algebra have been prepared according to the Civil Engineering (CE) exam syllabus.
Information about Vector Space - Linear Algebra covers all important topics for Civil Engineering (CE) 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Vector Space - Linear Algebra.
Introduction of Vector Space - Linear Algebra in English is available as part of our Engineering Mathematics for Civil Engineering (CE) & Vector Space - Linear Algebra in
Hindi for Engineering Mathematics course. Download more important topics related with notes, lectures and mock test series for
Civil Engineering (CE) Exam by signing up for free.
Description
Video Lecture & Questions for Vector Space - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE) - Civil Engineering (CE) full syllabus preparation | Free video for Civil Engineering (CE) exam to prepare for Engineering Mathematics.
Information about Vector Space - Linear Algebra
Here you can find the meaning of Vector Space - Linear Algebra defined & explained in the simplest way possible.
Besides explaining types of Vector Space - Linear Algebra theory, EduRev gives you an ample number of questions to practice Vector Space - Linear Algebra tests,
examples and also practice Civil Engineering (CE) tests.
|
65 videos|120 docs|94 tests
|
|
Explore Courses for Civil Engineering (CE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
Sample Paper
,Previous Year Questions with Solutions
,ppt
,past year papers
,Viva Questions
,MCQs
,Free
,Extra Questions
,Vector Space - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,practice quizzes
,mock tests for examination
,Important questions
,Semester Notes
,study material
,Exam
,Vector Space - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,Objective type Questions
,shortcuts and tricks
,Vector Space - Linear Algebra Video Lecture | Engineering Mathematics - Civil Engineering (CE)
,video lectures
,Summary
;
Study Vector Space - Linear Algebra on the App
Students of Civil Engineering (CE) can study Vector Space - Linear Algebra alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Vector Space - Linear Algebra,
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 Space - Linear Algebra is prepared as per the latest Civil Engineering (CE) 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