Math 232 - Linear Algebra

Prerequisites:

MATH151 or MATH154 or MATH157

Textbook:

Linear Algebra (Third Edition) by Fraleigh and Beauregard, Addison Wesley.

 

Course Description:

Matrix arithmetic, linear equations, and determinants. Real vector spaces and linear transformations. Inner products and orthogonality. Eigenvalues and eigenvectors.

 

Topics of study:

1. Linear Systems

(a) Matrices and their algebra

(b) Solving Systems of Linear Equations

(c) Inverses of Square Matrices

(d) Homogeneous Systems

(e) Applications to Population Distribution and Binary Codes

(f) Practical Considerations for Solving Large Systems

2. Vector Spaces

(a) Euclidean n-space

(c) Basis, Rank, Dimension and Independence

(b) Linear Transformations

(d) Vector space axioms

(e) Coordinatization of vectors

(f) Inner product spaces

3. Determinants

(a) Areas, Volumes and Cross Products

(b) Computation of Determinants

(c) Volume-change Factor of a Linear Transformation (d) Cramer’s Rule

4. Eigenvalues and Eigenvectors

(a) Diagonalization

(b) Applications to Markov chains and the Fibonacci sequence.

(c) Computation of Eigenvalues and Eigenvectors

5. Orthogonality

(a) Projections

(b) The Gram-Schmidt Process

(c) The Method of Least Squares

6. Similarity

(a) Change of basis

(b) Matrix Representations and Similarity

Students should be aware that they have certain rights to confidentiality concerning the return of course papers and the posting of marks. Please pay careful attention to the options presented in class at the beginning of the semester.