MATH 220 Linear Algebra

5 credits

Linear algebra serves as an introduction to matrix theory. Topics include matrix operations, determinants, solving systems of equations, n-dimensional vector spaces, subspaces, linear transformations, eigenvalues and eigenvectors, and their applications.

Prerequisites: MATH& 142

Course Outcomes
Upon successful completion of this course students will be able to:

Perform matrix operations, calculate determinants, find inverses for matrices (where possible), and find the transpose of a matrix
Use elementary row operations to solve systems of linear equations using Gaussian Elimination and Gauss-Jordan reduction methods
Identify a system of linear equations as independent, inconsistent, or dependent
Perform vector operations, use properties of vector operations, and determine vector subspaces, spanning sets, and bases of vector spaces
Show that a set of vectors forms the basis for a set, and find the dimension of a subspace
Find inner products and find a basis for a given inner product space
Use matrices to perform transformations between vector spaces and to identify isomorphisms
Find the kernel, range, rank, and nullity of a linear transformation
Find the standard matrix for a given linear transformation and use this matrix to find the image of a given vector
Find real eigenvalues and eigenvectors of a square matrix
Diagonalize symmetric matrices
Use the mathematical critical thinking skills of problem solving, pattern recognition, substitution, following structural rules, and quantitative modeling to solve problems requiring reasoning, critical thinking, and computation

Global Outcomes
This course teaches to the global outcome of critical thinking.

Total Hours: 50 Lecture Hours: 50