MATH 230 Matrix Algebra with Applications

5 credits

This course serves as an introduction to matrix theory and linear algebra. Topics covered include systems of equations, Gaussian elimination, LU decomposition, Euclidean vector spaces and subpaces, linear transformations, basis sets and dimensions, span of a vector space, Gram-Schmidt orthogonalization, least squares methods, eigenvalues, and eigenvectors. Applications are emphasized.

This course meets the Quantitative Reasoning general education distribution requirement.

Prerequisites: MATH& 163 (or concurrent enrollment)

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
Apply LU decomposition methods to factorize a matrix
Identify a system of linear equations as independent, inconsistent, or dependent
Identify properties of Euclidean vector spaces and the effects of linear transformations
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
Use Gram-Schmidt orthogonalization to find orthonormal vectors
Apply QR decomposition methods to factorize a matrix
Find real eigenvalues and eigenvectors of a square matrix
Diagonalize symmetric matrices
Apply matrix algebra to data fitting and least squares analysis
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

College-Wide Learning Outcomes
This course teaches to the college-wide learning outcome of Critical Thinking, the ability to evaluate information, draw inferences, arrive at conclusions, and create solutions based on objective analysis of the evidence.

Total Hours: 50 Theory (Lecture) Hours: 50