Gaussian Elimination is a method used to solve systems of linear equations by systematically eliminating variables until a unique solution is found.
The steps involved in Gaussian Elimination are:
1. Write the system of equations in matrix form
2. Use row operations to convert the matrix into an upper triangular form
3. Use back substitution to solve for the variables starting from the bottom row
4. Check the solution by plugging it back into the original equations.
The purpose of Gaussian Elimination is to solve systems of linear equations. It is particularly useful in solving large systems of equations where manual calculations would be time-consuming and prone to errors.
Gaussian Elimination can only be used for systems of linear equations. It also requires that the system has a unique solution, meaning that the equations are not dependent or inconsistent. It is also not suitable for systems with a large number of variables or equations as it can be computationally expensive.
Gaussian Elimination is a foundational method used in linear algebra and is often used as a precursor to more advanced methods such as LU decomposition and Cholesky decomposition. It is also closely related to other methods of solving equations such as Gauss-Jordan elimination and Cramer's rule.