1484?Milentije said:
Gaussian elimination is a method used to solve systems of linear equations. It involves transforming the system into an equivalent, triangular system through a series of row operations. This allows for easy back substitution to find the solutions to the system.
The purpose of Gaussian elimination is to find the solutions to a system of linear equations in a more efficient and organized manner. It eliminates the need for guess and check methods and allows for a systematic approach to solving the system.
Gaussian elimination works by performing row operations on a matrix representing the system of equations. These operations include multiplying a row by a constant, adding or subtracting one row from another, and swapping rows. The goal is to transform the matrix into an upper triangular form, where the only non-zero entries are on or above the main diagonal.
In partial Gaussian elimination, only the entries below the main diagonal are eliminated to create the upper triangular form. In full Gaussian elimination, both above and below the diagonal are eliminated. Full Gaussian elimination is typically used when the system has no exact solution and partial Gaussian elimination is used when an exact solution exists.
Gaussian elimination has several benefits, including its ability to solve systems of equations efficiently, its systematic approach, and its ability to handle large systems. It also provides a way to check for inconsistent or dependent systems and can be easily programmed for use in computers.