M 221 - Introduction to Linear Algebra

Credit(s): 4

Corequisite(s): M 171 or Math Department consent.
The study of vectors in the plane and space, systems of linear equations, matrices, determinants, linear transformations, eigenvalues, and eigenvectors. Calculators and/or computers are used where appropriate. (Spring Semester)

Course Learning Outcomes: Upon completion of the course, students will be able to

Solve linear systems of equations using Gauss-Jordan elimination and LU factorization with back and forward substitution;
State conditions that guarantee the solvability of linear systems and use these conditions to classify linear systems as having one, no, or infinitely many solutions;outline the fundamental properties of matrix algebra;
Compute determinants using the cofactor method and by reducing a matrix to triangular form;
Restate the definition of vector spaces and use this definition to recognize examples of vector spaces
Interpret matrices as linear transformations, develop a definition of orthogonality (both in terms of vectors and vector subspaces), explain the orthogonality relationships between the fundamental subspaces of a matrix, and use the gram-schmidt algorithm to create an orthogonal basis;
Compute the eigenvalues and eigenvectors of a matrix, diagonalize a matrix, and use the diagonalized structure to predict the qualitative dynamics of discrete or continuous dynamical systems;
Illustrate applications of linear algebra by solving problems in fields that could include (but aren’t limited to) nonlinear dynamics, image processing and compression, fitting models to experimental data, etc.; and
Write and read simple proofs.