Teddy's Presentation

Once again our good friend teddy has imparted a special gift upon us. I don't know how to get rid of this underscore but whatever. Here we go teddy! 

Elementary row options

1. Interchange two equations
2  Multiply an equation by a nonzero equation
3. Add a multiple of an equation to another equation.


Row-echelon form: the necessary form we need for augmented matrices and system of equations.
1. Rows consisting of zeroes belong at the bottom
2. First nonzero has a 1
3. For each row the leading 1 in the higher row is to the left of the lower one.

Here are some examples of matrices in row-echelon form:

How to solve system of equations through Gaussian elimination with back substitution.

1. Get the matrix in row-echelon form using elementary row operations
2. Use back substitution to solve for each variable.

Gauss-Jordan elimination

1. Obtain the reduced row-echelon form using elementary row operations.
2. Variables are equal to the coefficients on the right.