Theory and applications of systems of linear equations, vector spaces, and linear transformations. Fundamental concepts include: linear independence, basis, and dimension; orthogonality, projections, and least squares solutions of inconsistent systems; eigenvalues, eigenvectors, and applications to Markov chains, difference equations, and quadratic forms.
Athena Title
Introduction to Linear Algebra
Equivalent Courses
Not open to students with credit in MATH 3300, MATH 3300E
Prerequisite
MATH 3200 or MATH 3200W or CSCI 2610 or CSCI 2610E
Semester Course Offered
Offered fall
Grading System
A - F (Traditional)
Student Learning Outcomes
Students will be able to solve systems of linear equations by means of Gaussian elimination.
Students will be able to calculate the inverse of a matrix.
Students will be able to determine the projection operator onto a subspace.
Students will be able to determine the null space and range space of a linear transformation.
Students will be able to find eigenvalues and eigenvectors of a linear transformation, and determine if that linear transformation is diagonalizable.
Students will be able to prove elementary facts about vector spaces and linear transformations.
Topical Outline
Vector algebra and geometry. Dot products.
Matrices, echelon forms, and solution of systems of linear equations. Applications.
Matrix algebra: product, inverse, and transpose.
Subspaces: nullspace, rowspace, column space of a matrix.
Linear independence, basis, and dimension, orthogonal complement.
Linear transformations, projections and the least-squares solution. Gram-Schmidt process. Change of basis formula.
Determinants: signed area and volume, relation to invertibility.
Eigenvalues and eigenvectors, diagonalizability, applications to Markov processes and differential equations. Spectral theorem.
