Mathematics Exam > Mathematics Videos > Mathematics for Competitive Exams > System of Linear Equations: Homogeneous Equation
System of Linear Equations: Homogeneous Equation Video Lecture | Mathematics for Competitive Exams
|
98 videos|27 docs|30 tests
|
FAQs on System of Linear Equations: Homogeneous Equation Video Lecture - Mathematics for Competitive Exams
| 1. What is a homogeneous equation in a system of linear equations? |  |
Ans. In a system of linear equations, a homogeneous equation is one where all the constant terms on the right side of the equations are zero. It can be represented as Ax = 0, where A is the coefficient matrix and x is the variable vector.
| 2. How do you determine the number of solutions for a homogeneous system of linear equations? | |
Ans. The number of solutions for a homogeneous system of linear equations depends on the number of variables and the number of equations. If the number of variables is greater than the number of equations, then the system will have infinitely many solutions. If the number of variables is less than the number of equations, then the system will have a unique solution (trivial solution) where all variables are zero.
| 3. Can a homogeneous system of linear equations have a non-trivial solution? | |
Ans. Yes, a homogeneous system of linear equations can have a non-trivial solution. A non-trivial solution is a solution where at least one variable is not equal to zero. If the system has infinitely many solutions, then there will be infinitely many non-trivial solutions.
| 4. What is the relationship between the homogeneous equation and the trivial solution? | |
Ans. The trivial solution in a homogeneous equation is when all variables are equal to zero. In other words, it is the solution where no variable has a non-zero value. The trivial solution always exists in a homogeneous equation because substituting zero for all variables satisfies the equation.
| 5. How can a homogeneous system of linear equations be solved? | |
Ans. To solve a homogeneous system of linear equations, one can first write the system in matrix form as Ax = 0, where A is the coefficient matrix and x is the variable vector. Then, using techniques such as row operations or matrix inverse, the reduced row echelon form of the augmented matrix can be obtained. The solutions can be determined by expressing the variables in terms of free variables in the system.
Related Exams
About this Video
|
4.91/5 Rating |
|
Dec 23, 2024 Last updated |
Video Description: System of Linear Equations: Homogeneous Equation for Mathematics 2024 is part of Mathematics for Competitive Exams preparation.
The notes and questions for System of Linear Equations: Homogeneous Equation have been prepared according to the Mathematics exam syllabus.
Information about System of Linear Equations: Homogeneous Equation covers all important topics for Mathematics 2024 Exam.
Find important definitions, questions, notes, meanings, examples, exercises and tests below for System of Linear Equations: Homogeneous Equation.
Introduction of System of Linear Equations: Homogeneous Equation in English is available as part of our Mathematics for Competitive Exams for Mathematics & System of Linear Equations: Homogeneous Equation 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 System of Linear Equations: Homogeneous Equation Video Lecture | Mathematics for Competitive Exams - Mathematics full syllabus preparation | Free video for Mathematics exam to prepare for Mathematics for Competitive Exams.
Information about System of Linear Equations: Homogeneous Equation
Here you can find the meaning of System of Linear Equations: Homogeneous Equation defined & explained in the simplest way possible.
Besides explaining types of System of Linear Equations: Homogeneous Equation theory, EduRev gives you an ample number of questions to practice System of Linear Equations: Homogeneous Equation 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
Free
,Viva Questions
,ppt
,Important questions
,past year papers
,study material
,Semester Notes
,shortcuts and tricks
,mock tests for examination
,Objective type Questions
,Extra Questions
,Exam
,practice quizzes
,video lectures
,Sample Paper
,MCQs
,Previous Year Questions with Solutions
,System of Linear Equations: Homogeneous Equation Video Lecture | Mathematics for Competitive Exams
,System of Linear Equations: Homogeneous Equation Video Lecture | Mathematics for Competitive Exams
,Summary
,System of Linear Equations: Homogeneous Equation Video Lecture | Mathematics for Competitive Exams
;
Study System of Linear Equations: Homogeneous Equation on the App
Students of Mathematics can study System of Linear Equations: Homogeneous Equation alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the System of Linear Equations: Homogeneous Equation,
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 System of Linear Equations: Homogeneous Equation 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