MATH 220 - Linear Algebra

Credits: 5
LEC hours per week: 5
MATH 220 designed for students planning to major in mathematics, engineering, computer science, or physics. Topics include systems of linear equations, matrices, eigenvalues, eigenvectors, vector spaces, linear transformations, orthogonality and diagonalization.
Prerequisite(s): A grade of C- or higher in MATH& 153, satisfactory placement, or permission of the Math Department.
Course Outcomes:

Use matrices to solve systems of linear equations and vector equations.
Add, subtract, multiply, invert, and factor matrices.
Analyze the linear independence of a set of vectors and determine a basis for a vector space.
Find eigenvalues and eigenvectors and use them to diagonalize matrices.
Analyze linear transformations and interpret them geometrically in R2 and R3 when applicable.
Apply the Gram-Schmidt process to produce an orthogonal basis for a vector space.
Find least-squares solutions.
Access and use technology including a computer algebra system.
Communicate mathematics using appropriate vocabulary and notation.

Course Topics:

Systems of linear equations
Matrix dperations, determinants, inverses, row space, column space, nullspace, rank, diagonalization, LU factorization, QR factorization
Gaussian elimination, row operations, echelon forms Matrix and vector equations
Linear combinations of vectors, linear independence of vectors, geometry of vectors in R2 and R3
Eigenvalues, eigenvectors, eigenspaces, eigenbases
Vector spaces, subspaces, bases, dimension, coordinate systems, change of basis
Linear transformations, domain, codomain, range, image, kernel
Orthogonality, G ram-schmidt process, least-squares solutions

Course Attribute(s): Natural Science, Quantitative