Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > Rank of Matrix
Rank of Matrix Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on Rank of Matrix Video Lecture - Mathematics for Competitive Exams
| 1. What is the rank of a matrix? |  |
Ans. The rank of a matrix is the maximum number of linearly independent rows or columns in the matrix. It represents the dimension of the vector space spanned by the rows or columns of the matrix.
| 2. How can the rank of a matrix be calculated? | |
Ans. The rank of a matrix can be calculated by performing row operations to reduce the matrix to its row-echelon form or reduced row-echelon form. The number of non-zero rows in the row-echelon form or reduced row-echelon form will give the rank of the matrix.
| 3. Can the rank of a matrix be greater than its number of rows or columns? | |
Ans. No, the rank of a matrix cannot be greater than its number of rows or columns. The rank of a matrix is always less than or equal to the minimum of the number of rows and columns in the matrix.
| 4. What does a matrix with full rank mean? | |
Ans. A matrix is said to have full rank if its rank is equal to the minimum of its number of rows and columns. In other words, a matrix with full rank has linearly independent rows and columns, and its columns span the entire column space.
| 5. How does the rank of a matrix affect its solutions in a system of linear equations? | |
Ans. The rank of a matrix is closely related to the number of solutions in a system of linear equations. If the rank of the coefficient matrix is equal to the rank of the augmented matrix, the system has a unique solution. If the rank of the coefficient matrix is less than the rank of the augmented matrix, the system has infinitely many solutions. If the rank of the coefficient matrix is less than the number of variables, the system has no solution.
Related Exams
About this Video
|
4.82/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: Rank of Matrix for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for Rank of Matrix have been prepared according to the Mathematics exam syllabus.
Information about Rank of Matrix covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for Rank of Matrix.
Introduction of Rank of Matrix in English is available as part of our Mathematics for Competitive Exams for Mathematics & Rank of Matrix 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 Rank of Matrix Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about Rank of Matrix
Here you can find the meaning of Rank of Matrix defined & explained in the simplest way possible.
Besides explaining types of Rank of Matrix theory, EduRev gives you an ample number of questions to practice Rank of Matrix 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
Previous Year Questions with Solutions
,Extra Questions
,past year papers
,Rank of Matrix Video Lecture | Mathematics for Competitive Exams
,Important questions
,mock tests for examination
,Objective type Questions
,video lectures
,Summary
,Rank of Matrix Video Lecture | Mathematics for Competitive Exams
,Sample Paper
,Viva Questions
,practice quizzes
,ppt
,MCQs
,study material
,Free
,shortcuts and tricks
,Rank of Matrix Video Lecture | Mathematics for Competitive Exams
,Semester Notes
,Exam
;
Study Rank of Matrix on the App
Students of Mathematics can study Rank of Matrix alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the Rank of Matrix,
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 Rank of Matrix 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