Review: 8.1-Matrices and Systems of Equations

Teddy did his presentation on matrices and systems of equations. Here is a quick run-down on this section.

We can find the solutions of matrices by getting them into row-echelon form using the elementary row operations and/or back substitution.

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.

Math joke of the day: