Notes for 8.1 presentation

8.1: matrices and systems of equations
Vocabulary
Matrix: a rectangular array that displays series of terms through m rows and n columns.
Augmented matrix: matrix derived from a system of linear equations. Elementary row options: the means in which we can rearrange matrices. 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 mainly 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.

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.