LINEAR ALGEBRA

MA 260

Catalogue Description

Algebra of matrices and vector spaces and applications to the solutions of systems of linear equations and geometric transformations are studied in this course. 3 credits. Prerequisites: MATH 191 Calculus II or equivalent.

Goals

A. To introduce the student to basic notions of Matrices, Determinants, Vector Spaces, and Linear Transformations, as well as to the connections among these topics.

B. To introduce the student to Theorems, their proofs and applications, in order to familiarize the student with the language of Modern Math.

C. To introduce the student to Graphing Calculators and one or more Linear Algebra Computer Software.

Procedures

A. Lecture/Discussion

B. Readings

C. Assigned Problems

D. Computer Software Supplements in Math Resource Center.

Course Content

A. Linear Systems and Matrices

1. Introduction

2. Matrices and Gaussian Elimination

3. Gauss-Jordan Elimination

4. Matrix Operations

5. Inverses of Matrices

B. Determinants

1. 2 x 2 Determinants

2. Higher-order Determinants

3. Determinants and Elementary Row Operations

4. Cramer's Rule and Inverse Matrices

C. Vectors in the Plane and in Space

1. The Vector Space R2

2. The Vector Space R3

3. Orthogonality and the Dot Product

4. Lines and Planes in Space

D. Vector Spaces

1. The Vector Space Rn and Subspaces

2. Linear Combinations and Linear Independence

3. Bases for Vector Spaces

4. Row and Column Spaces

E. Orthogonality and Least Squares

1. Orthogonal Vectors in Rn

2. Orthogonal Projections and Least Squares Solutions

3. Orthogonal Bases and the Gran-Schmidt Algorithm

F. Eigenvalues and Eigenvectors

1. Introduction

2. Diagonalization of Matrices

3. Applications to Powers of a Matrix

4. Symmetric Matrices and Orthogonal Eigenvectors

G. Linear Transformations

1. Matrix Transformations

2. Properties or Linear Transformations

3. Coordinates and Change of Basis

H. Further Applications

1. Quadratic Forms and Conic Sections

I. Use of Computers and Graphing Calculators in Conjunction with Linear Algebra

Evaluation Methods

1. Tests - Three Examinations - Each 20% of Grade

2. Classwork/Attendance

3. Assignments

4. Computer Lab - 15% of Grade

5. Comprehensive Final Exam - 25% of Grade

Bibliography

Required Text: Larson, Roland E. & Edwards, Bruce H., Elementary Linear Algebra, 2nd Ed., D.C. Heath & Co., 1991.

Nicholson, W. Keith, Elementary Linear Algebra With Applications, PWS-Kent, Boston, Mass., 1990.

Noble, B. & Daniel, J., Applied Linear Algebra, 3rd Ed., Prentice Hall, 1988.

Stegher, M., Linear Algebra, Harper & Row, New York, N.Y., 1988.

Software

Orzech, Morris, Matrix Pad, D.C. Heath & Co., New York, N.Y., 1988.

DERIVE - A Mathematical Assistant, Soft Warehouse, Inc., Honolulu, Hawaii