Standards: Chapter 1

I can determine whether a point or a vector is a solution to a system
of linear equations.

I can convert linear systems to augmented matrices and vice versa. I
can solve systems of linear equations using row operations. I can use
Gaussian elimination with back-substitution to solve systems of linear
equations. I can use Gauss-Jordan elimination to solve systems of
linear equations.

I can express solutions to linear systems in general form and
parametric form and, in 2 or 3 variables, characterize the solution
sets geometrically.

I can characterize the solutions to systems of linear equations using
appropriate notation and vocabulary (e.g., consistent or inconsistent
systems, free parameters or variables, leading variables.) I
understand the trichotomy of possible solutions algebraically. I can
recognize when a linear system is in echelon form or reduced echelon
form algebraically.

I understand the trichotomy of possible solutions to systems of linear
equations geometrically. In 2 or 3 variables, I can recognize when a
consistent linear system is in echelon form geometrically.