Gaussian Elimination

Gaussian Elimination

by Elmo

​Gaussian Elimination in row echelon form.

​Card Friedrich Gauss, original name Johann Friedrich Card Gauss, German mathematician, generally regarded as one of the greatest mathematicians of all time for his contributions to number theory, geometry, probability theory, geodesy, planetary astronomy, the theory of functions, and potential theory (including electromagnetism).

​Operations that produce equivalent systems:

​Each of the following operations on a system of linear equations produces an equivalent system. Two systems of linear equations are equivalent when they have the same solution set. To solve a system that is not in row-echelon form. First convert it to an equivalent system that is in row-echelon form by using the operation listed:

1. Interchange two equations

2. Multiply an equations by a non-zero constant.

3. Add a multiple of an equation to another equation.

​Example:

Solve the following using Gaussian elimination:

​The augmented matrix is

​Divide first row by 2 and divide second row by 2:

​Subtract 7 times first row from third row:

second row to the third row:​

​Multiply third row by

​By back-substitution:

​That's all.

​Thank you for listening.