MATH 228 is a proof-based course in linear algebra, covering systems of linear equations, matrices, determinants, finite dimensional vector spaces, and linear transformations. The least-squares problem and eigenvalues/eigenvectors are typically covered towards the end of the class. Although there is a computational component to the class, a stronger focus is put on developing well written proofs, which may include the properties of matrix algebra, set containment, linear independence, and properties of vector spaces and subspaces. The figure to the left shows the intersection of three planes in three dimensional space, i.e. a 3x3 linear system with a unique solution.