Catalog Course Search Details

 Department:    MATH

 Course #:    204

 Credits:    5

 Variable:     No

 IUs:    5

 CIP:    270101

 EPC:    n/a

 REV:    2021

 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  

Prerequisite: MATH& 151 with a "C" or higher.

Contact Hours (based on 11 week quarter)

Lecture: 55

Lab: 0

Other: 0

Systems: 0

Clinical: 0

Intent: Distribution Requirement(s) Status:  

Academic Elective  

Equivalencies At Other Institutions

Learning Outcomes

After completing this course, the student will be able to:

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

General Education Learning Values & Outcomes

Revised August 2008 and affects outlines for 2008 year 1 and later.

Course Contents

1. 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
2. Determinants
   • Determinants by co-factor expansion
   • Calculating determinants by row reduction
   • Properties of determinants
3. 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
4. Eigensystems
   • Eigenvalues and eigenvectors
   • The characteristic equation
   • Diagonalization
   • Complex eigenvalues
5. 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