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.
