Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Properties of Determinants of Matrices
Properties of Determinants of Matrices Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Properties of Determinants of Matrices Video Lecture - Mathematics for Competitive Exams
| 1. What is the determinant of a matrix? |  |
Ans. The determinant of a matrix is a scalar value that can be calculated for square matrices only. It represents certain properties of the matrix and is denoted by "det(A)" or "|A|".
| 2. How is the determinant of a matrix calculated? | |
Ans. The determinant of a matrix can be calculated using various methods, such as expansion by minors, cofactor expansion, or using row operations. The specific method used depends on the size of the matrix and the available information.
| 3. What are the properties of determinants of matrices? | |
Ans. The properties of determinants of matrices include:
1. Property of Linearity: The determinant of a sum of matrices is equal to the sum of their determinants.
2. Property of Scalar Multiplication: Multiplying a matrix by a scalar multiplies its determinant by the same scalar.
3. Property of Transposition: The determinant of a matrix is the same as the determinant of its transpose.
4. Property of Row or Column Interchange: Interchanging any two rows or columns of a matrix changes the sign of its determinant.
5. Property of Row or Column Multiplication: Multiplying any row or column of a matrix by a scalar multiplies its determinant by the same scalar.
| 4. How does the determinant of a matrix relate to invertibility? | |
Ans. The determinant of a matrix is directly related to its invertibility. If the determinant is non-zero, the matrix is said to be invertible or non-singular. In this case, the matrix has a unique inverse. On the other hand, if the determinant is zero, the matrix is said to be singular or non-invertible, and it does not have an inverse.
| 5. Can the determinant of a matrix be negative? | |
Ans. Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the number of row or column interchanges required to transform the matrix into its row-echelon form. If an odd number of interchanges is performed, the determinant is negative; otherwise, it is positive.
Related Exams
About this Video
|
4.98/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Properties of Determinants of Matrices for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Properties of Determinants of Matrices have been prepared according to the Mathematics exam syllabus.
Information about Properties of Determinants of Matrices covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Properties of Determinants of Matrices.
Introduction of Properties of Determinants of Matrices in English is available as part of our Mathematics for Competitive Exams for Mathematics & Properties of Determinants of Matrices 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 Properties of Determinants of Matrices Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Properties of Determinants of Matrices
Here you can find the meaning of Properties of Determinants of Matrices defined & explained in the simplest way possible.
Besides explaining types of Properties of Determinants of Matrices theory, EduRev gives you an ample number of questions to practice Properties of Determinants of Matrices 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
MCQs
,Previous Year Questions with Solutions
,ppt
,Properties of Determinants of Matrices Video Lecture | Mathematics for Competitive Exams
,shortcuts and tricks
,Semester Notes
,past year papers
,practice quizzes
,mock tests for examination
,Exam
,Important questions
,Viva Questions
,study material
,video lectures
,Summary
,Objective type Questions
,Extra Questions
,Properties of Determinants of Matrices Video Lecture | Mathematics for Competitive Exams
,Properties of Determinants of Matrices Video Lecture | Mathematics for Competitive Exams
,Free
,Sample Paper
;
Study Properties of Determinants of Matrices on the App
Students of Mathematics can study Properties of Determinants of Matrices alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Properties of Determinants of Matrices,
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 Determinants of Matrices 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