Gaussian Elimination

Gaussian Elimination is performed to certain augmented matrices so that they can be in a row-echelon form. 

Steps
*From a System, transform it to an augmented matrix. 
*Perform Elementary Row Operations to transform it to Row-Echelon form.
*Do back-substitution.

3 Elementary Row Operations
1. Interchanging 2 rows.

2. Multiplying a row by a nonzero constant.
3. Adding a multiple of a row to another row. 

How to Know if the matrix is in Row-Echelon Form or not?

a. Rows with zero entries must be at the bottom of the matrix. 

b. All leading coefficients must be 1.
c. The leading coefficient of the higher row must be further to the left than the leading coefficient of the lower row.