Solve systems of linear equations and describe their solution sets;
use matrices to represent a system of linear equations, reduce matrices to their echelon form, and carry out the relevant allowed operations with matrices;
relate the concepts of linear independence and spanning to systems of linear equations, as well as one-to-one or onto linear transformations;
determine when a square matrix is invertible;
use subspaces to generalize solution sets of homogeneous systems, and define the size (dimension) of subspaces;
compute the determinant of a matrix, and use determinants to find eigenvalues and eigenvectors of a matrix;
determine when a square matrix is diagonalizable, and find such a diagonalization when one exists;
use linear algebra to answer questions regarding length, angle, and orthogonal projections;
use orthogonal projections to find the value of a set of parameters from a model that "best fits" data;
translate between numerical, algebraic, and geometric interpretations and/or representations of the above concepts and skills.
Have fun and gain confidence in your mathematical reasoning and skills
Improve as a learner, teacher, communicator, and mathematician by working individually and as part of a community to further not only your personal growth, but also our collective knowledge and understanding of the world around us
read and communicate (verbally and in writing) clearly, concisely, and correctly using relevant vocabulary, notation, and colloquial language of modern mathematics
understand and appreciate philosophical and conceptual ideas of modern mathematics, and how they lead to models for, and solutions of, common (and uncommon) problems