How to compute all solutions to a general system $Ax=b$ of linear equations and connection to the corresponding homogeneous system $Ax=0$. Visualization of the geometry of solution sets. Consistent systems and their solution using row reduction.
Homogeneous systems of linear equations; trivial versus nontrivial solutions of homogeneous systems; how to find nontrivial solutions; how to know from the reduced row-echelon form of a matrix whether the corresponding homogeneous system has nontrivial solutions.
Pre-class quiz (three questions) on determining the solution set of a linear system, given an augmented matrix in row-echelon or reduced row-echelon form. To be completed by students after having watched a pre-class video on the topic.