A homogenous linear system is a set of equations in which all variables have a coefficient of zero on one side of the equation. This means that the system has a solution of all zeros, making it a "trivial" solution.
A non-homogenous linear system is one in which at least one of the equations has a non-zero constant term on one side, making it a "non-trivial" solution. This means that the system has a solution other than all zeros.
The purpose of solving a homogenous linear system is to find the values of the variables that satisfy all of the equations in the system. This can help to model and solve real-world problems in fields such as physics, economics, and engineering.
To solve a homogenous linear system, you can use methods such as substitution, elimination, or matrix operations. These methods involve manipulating the equations to eliminate variables and solve for the remaining variables.
Studying homogenous linear systems is important in mathematics because it helps to develop problem-solving skills and critical thinking. It also serves as a foundation for more advanced concepts in linear algebra and differential equations.