Preparation for Quiz: (Quiz will be on Tuesday August 30)

Essential Material:

Read Sections 1.1 - 1.3

Key Terms:  linear equation, coefficient, system of linear equations, solution set, row equivalence, equivalent systems, consistent vs. inconsistent, coefficient matrix, augmented matrix, elementary row operation, row echelon form, reduced row echelon form, pivot position, pivot column, forward phase, backward phase, basic variable, free variable, general solution, parametric description of solution set, back-substitution, column vector, linear combination, span.

Techniques:

• Write a system of linear equations as an augmented matrix
• Perform an elimination procedure to solve a system of equations
• Use elementary row operations to reduce a an augmented matrix to row echelon or reduced row echelon form.  Use the reduced row echelon form to solve the corresponding system of equations.  Use back substitution on the row echelon form to solve the corresponding system of equations.
• Find the general solution to a system of equations and write it using a parametric description.