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Spring 2019

Mathematics Courses:

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MAT246 - Linear Algebra

Credits: 4

Catalog Description: Covers systems of linear equations and matrices, determinants, vectors and vector spaces, linear transformations, eigenvectors and eigenvalues, linear transformations, and numerical methods. Four class hours. Prerequisite: MAT142 with a grade of C or better, or permission of instructor.

Lecture: 4 hrs.

Course Learning Outcomes (CLOs):
Upon successful completion of this course, as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, the student will be able to:


1. Solve a system of linear equations using Gauss-Jordan Elimination Method*
2.Perform matrix operations, including finding inverse matrices
3.Evaluate determinants and use Cramer's Rule to solve systems of linear equations
4.Perform vector operations
5.Evaluate a linear transformation or composition of transformations from Rm to Rn
6.Prove that a set of vectors form a linearly independent set
7.Identify basis and dimension of a general vector space
8.Find eigenvalues for a given matrix


* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.


Content Outline:
I. Matrices and Systems of Equations
A. The Elimination Method
B. Matrices and Matrix Operations
C. Inverses; Rules of Matrix Arithmetic
D. Diagonal, Triangular, & Symmetric Matrices

II. Determinants
A. The Determinant Functions
B. Cramer's Rule

III. Vectors in 2-space & 3-space
A. Introduction to Vectors
B. Vector Arithmetic
C. Lines and Planes in 3-Space


IV. Euclidean Vector Spaces
A. Euclidean n-space
B. Linear Transformations
C. Properties of Linear Transformations

V. General Vector Spaces
A. Real Vector Spaces
B. Subspaces
C. Linear Independence
D. Basis and Dimension
E. Rank and Nullity

VI. Eigenvalues, Eigenvectors
A. Eigenvalues & Eigenvectors
B. Diagonalization
C. Orthogonal Diagonalization

VII. Linear Transformations
A. General Linear Transformations
B. The Matrix of a Linear Transformation
C. Similarity

VIII. Additional Topics - Applications as time permits

Effective Term: Fall 2016