Mathematics Exam > Mathematics Videos > Algebra > Properties of Scalar Multiplication
Properties of Scalar Multiplication Video Lecture | Algebra - Mathematics
|
161 videos|58 docs
|
FAQs on Properties of Scalar Multiplication Video Lecture - Algebra - Mathematics
| 1. What is scalar multiplication? |  |
Ans. Scalar multiplication is an operation where a scalar (a real number) is multiplied to each element of a given vector. This operation results in a new vector with the same direction as the original vector but with a different magnitude.
| 2. How is scalar multiplication performed? | |
Ans. Scalar multiplication is performed by multiplying each component of the vector by the scalar. For example, if we have a vector [2, 4] and we want to multiply it by a scalar 3, the resulting vector would be [6, 12].
| 3. What are the properties of scalar multiplication? | |
Ans. The properties of scalar multiplication are as follows:
- Associativity: (a * b) * v = a * (b * v), where a and b are scalars and v is a vector.
- Distributivity with respect to addition: (a + b) * v = a * v + b * v, where a and b are scalars and v is a vector.
- Distributivity with respect to scalar addition: a * (v + w) = a * v + a * w, where a is a scalar and v, w are vectors.
- Identity element: 1 * v = v, where 1 is the multiplicative identity and v is a vector.
| 4. How does scalar multiplication affect the magnitude of a vector? | |
Ans. Scalar multiplication affects the magnitude of a vector by scaling it. If the scalar is greater than 1, the magnitude of the resulting vector will be greater than the magnitude of the original vector. If the scalar is between 0 and 1, the magnitude of the resulting vector will be smaller than the magnitude of the original vector. If the scalar is negative, the resulting vector will have the same magnitude as the original vector but will point in the opposite direction.
| 5. Can scalar multiplication change the direction of a vector? | |
Ans. No, scalar multiplication does not change the direction of a vector. It only scales the vector by multiplying it with a scalar. The resulting vector will have the same direction as the original vector, but its magnitude will be different depending on the scalar value.
Related Exams
About this Video
|
4.80/5 Rating |
|
Nov 08, 2024 Last updated |
Video Description: Properties of Scalar Multiplication for Mathematics 2024 is part of Algebra preparation.
The notes and questions for Properties of Scalar Multiplication have been prepared according to the Mathematics exam syllabus.
Information about Properties of Scalar Multiplication covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Properties of Scalar Multiplication.
Introduction of Properties of Scalar Multiplication in English is available as part of our Algebra for Mathematics & Properties of Scalar Multiplication in
Hindi for Algebra 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 Scalar Multiplication Video Lecture | Algebra - Mathematics - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Algebra.
Information about Properties of Scalar Multiplication
Here you can find the meaning of Properties of Scalar Multiplication defined & explained in the simplest way possible.
Besides explaining types of Properties of Scalar Multiplication theory, EduRev gives you an ample number of questions to practice Properties of Scalar Multiplication tests,
examples and also practice Mathematics tests.
|
161 videos|58 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
shortcuts and tricks
,Free
,mock tests for examination
,Exam
,Objective type Questions
,Summary
,Semester Notes
,MCQs
,Properties of Scalar Multiplication Video Lecture | Algebra - Mathematics
,Extra Questions
,Previous Year Questions with Solutions
,ppt
,Important questions
,Sample Paper
,study material
,past year papers
,video lectures
,practice quizzes
,Properties of Scalar Multiplication Video Lecture | Algebra - Mathematics
,Viva Questions
,Properties of Scalar Multiplication Video Lecture | Algebra - Mathematics
;
Study Properties of Scalar Multiplication on the App
Students of Mathematics can study Properties of Scalar Multiplication alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Properties of Scalar Multiplication,
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 Scalar Multiplication 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