MATH 204 - Elementary Linear Algebra

Credits: 5
Variable Credit Course: No

Lecture Hours: 55
Lab Hours: 0
Worksite/Clinical Hours: 0
Other Hours (LIA/Internships): 0

Course Description: Introduction to linear algebra covering systems of linear equations, matrices, vector spaces and subspaces, spanning sets, eigenvalues and eigenvectors, transformations, determinants and applications. Graphing Technology required.

Prerequisite: MATH& 151 with a C or higher.
Meets FQE Requirement: No
Elective Requirements: Fulfills Academic Electives
Integrative Experience Requirement: No

Student Learning Outcomes

Solve systems of equations using Gauss-Jordan elimination.
Reduce a matrix to row-reduced echelon form using row reduction.
Test for linear independence in Rn.
Reduce a spanning set to a basis in Rn.
Compute the row space, column space, and null space of a matrix.
Compute a basis for the kernel and image of a linear transformation.
Factor a matrix using LU factorization and by diagonalization.
Compute the eigenvalues and eigenvectors of a matrix.

Course Contents

Linear Systems of Equations and Matrices. Gauss Jordan row reduction. Vector equations. Matrices and matrix operations. Inverse of a matrix. Elementary matrices and the inverse matrix. Matrix of a linear transformation. Characterizations of invertible matrices. Linear independence in Rn. LU factorization of a matrix.
Determinants. Determinants by co-factor expansion. Calculating determinants by row reduction. Properties of determinants.
General Vector Spaces. Vector spaces and subspaces. Linear independence. Coordinate systems. Change of basis. Dimensions of a vector space. Rank and nullity. Matrix transformations from Rn to Rm.
Eigensystems. Eigenvalues and eigenvectors. The characteristic equation. Diagonalization. Complex eigenvalues.
Optional Applications. Cramer’s Rule. Markov chains. Leontief Input-Output model. Applications to computer graphics. Kirchhoff’s Law. Difference equations. Networks. Orthogonality and least squares. Curve fitting. Linear programming.

Instructional Units: 5