Yuba Community College District
Yuba College Course Outline
Course Information
Course Number:
MATH 3
Full Course Title:
Linear Algebra
Short Title:
Linear Algebra
Effective Term:
Fall 2013
Course Standards
Lecture Hours:
54.000
Total Units:
3.000
Total Hours:
54.00
Repeatable:
No
Grading Method:
Letter Grade Only
Minimum Qualifications
 Mathematics (Masters Required)
Course Description
This course develops the techniques and theory needed to solve and classify systems of linear equations. Solution techniques include row operations, Gaussian elimination, and matrix algebra. Investigates the properties of vectors in two and three dimensions, leading to the notion of an abstract vector space. Vector space and matrix theory are presented including topics such as inner products, norms, orthogonality, eigenvalues, eigenspaces, and linear transformations. Selected applications of linear algebra are included.Conditions of Enrollment
Completion with a C or better in: MATH 1B. Other: Recommended successful completion of Math 1C.
Math 1C introduces vectors and a large part of Math 3 will be about vectors and vector spaces. Moreover, Math 1C (formerly Math 2A) was the prerequisite for Math 3 before the revision.
Advisories

Language  recommended eligibility for English 1A

Mathematics  recommended eligibility for Math 52
Content
Course Lecture Content
 Techniques for solving systems of linear equations including Gaussian and GaussJordan elimination and inverse matrices
 Matrix algebra, invertibility, and the transpose
 Relationship between coefficient matrix invertibility and solutions to a system of linear equations and the inverse matrices
 Special matrices: diagonal, triangular, and symmetric
 Determinants and their properties
 Vector algebra for Rn
 Real vector space and subspaces
 Linear independence and dependence
 Basis and dimension of a vector space
 Matrixgenerated spaces: row space, column space, null space, rank, nullity
 Change of basis
 Linear transformations, kernel and range, and inverse linear transformations
 Matrices of general linear transformations
 Eigenvalues, eigenvectors, eigenspace
 Diagonalization including orthogonal diagonalization of symmetric matrices
 Inner products on a real vector space
 Dot product, norm of a vector, angle between vectors, orthogonality of two vectors in Rn
 Angle and orthogonality in inner product spaces
 Orthogonal and orthonormal bases: GramSchmidt process
 Method of least squares
Objectives

Find solutions of systems of equations using various methods appropriate to lower division linear algebra.

Use bases and orthonormal bases to solve problems in linear algebra.

Find the dimension of spaces such as those associated with matrices and linear transformations.

Find eigenvalues and eigenvectors and use them in applications.
**Requires Critical Thinking**

Prove basic results in linear algebra using appropriate proofwriting techniques such as linear independence of vectors; properties of subspaces; linearity, injectivity and surjectivity of functions; and properties of eigenvectors and eigenvalues.
**Requires Critical Thinking**
Student Learning Outcomes
 Computation – Solve a system of linear equations using matrix methods.
 Computation – Calculate eigenvalues and eigenvectors for a 3x3 matrix.
 Critical Thinking – Formulate transformations between ndimensional vector spaces.
Methods of Instruction

Lecture/Discussion
Assignments
Hours per week on assignments outside of the class:
Reading Assignments
Writing Assignments
Methods of Evaluation
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes

OtherGroup or individual projects.
Course Materials
Textbooks:

Gilbert Strang. Introduction to Linear Algebra, 4th ed. Wellesley Cambridge Press, 2009, ISBN: 9780980232714Equivalent text is acceptable