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System of Linear Equations: Non-Homogeneous Equation Video Lecture | Mathematics for Competitive Exams
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FAQs on System of Linear Equations: Non-Homogeneous Equation Video Lecture - Mathematics for Competitive Exams
| 1. What is a non-homogeneous system of linear equations? |  |
Ans. A non-homogeneous system of linear equations is a set of equations where the constant term is nonzero. In other words, it is a system where the equations do not all equal zero when written in standard form.
| 2. How is a non-homogeneous system of linear equations different from a homogeneous system? | |
Ans. In a non-homogeneous system, at least one equation has a nonzero constant term, whereas in a homogeneous system, all equations have a constant term of zero. This difference affects the nature of the solutions and the methods used to solve the systems.
| 3. What methods can be used to solve a non-homogeneous system of linear equations? | |
Ans. There are several methods to solve a non-homogeneous system of linear equations, including the substitution method, the elimination method, and the matrix method. These techniques involve manipulating the equations to determine the values of the variables that satisfy all the equations simultaneously.
| 4. Can a non-homogeneous system have infinitely many solutions? | |
Ans. Yes, a non-homogeneous system can have infinitely many solutions if it is consistent and has more variables than equations. In such cases, there will be free variables that can take on any value, resulting in an infinite number of solutions.
| 5. Are there any real-world applications of non-homogeneous systems of linear equations? | |
Ans. Yes, non-homogeneous systems of linear equations have various real-world applications. For example, they can be used to model economic systems, electrical circuits, chemical reactions, and population dynamics. By solving these systems, we can gain insights into the behavior and relationships of the variables involved in these scenarios.
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Dec 23, 2024 Last updated |
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