What is Gaussian elimination?
Given: Gaussian elimination
Gaussian elimination, also known as row-reduction, is a technique used to solve systems of linear equations. The coefficients of the equations, including the constant are put in a matrix form.
Three types of operations are performed to create a matrix that has a diagonal of
The three operations are:
- swap two rows
- Multiply a row by a nonzero constant (scalar)
- Multiply a row by a nonzero number and add to another row
Simple example. Solve for
Multiply row 1 by
Replace row 2 with: Multiply row 1 by
Divide row 2 by
Use back substitution to solve for