### System Of Linear Equations

**System of Linear Equations Concepts**

**Linear Equation**:

-An equation that can be written in the form (ax + b = c), where (a, b,) and (c) are constants, and (x) is the variable.

**System of linear equations**:

-A set of two or more linear equations in the same variables.

**Solution to a system of linear equations**:

-A set of values for the variables that make all the equations in the system true.

**Consistent system of linear equations**:

-A system that has at least one solution.

**Inconsistent system of linear equations**:

-A system that has no solution.

**Methods of solving systems of linear equations**:

- Graphical method
- Substitution method
- Elimination method (Gaussian elimination)

## **Determinant**:
-A scalar value that can be used to determine whether a system of linear equations has a unique solution, no solutions, or infinitely many solutions.

**Cramer’s rule**:

-A method for finding the solution to a system of linear equations that has a unique solution.

**Rank of a matrix**:

-The maximum number of linearly independent rows or columns in a matrix.

**Eigenvalues and eigenvectors of a matrix**:

-The eigenvalues of a square matrix are the roots of its characteristic equation, and the eigenvectors are the corresponding eigenvectors.

**Applications of systems of linear equations**:

-Systems of linear equations can be used to solve problems in various fields, such as engineering, physics, economics, and computer science.