MATH 230 - Linear Algebra

3 Credits: (3 lecture)

Course Description
This is a course which provides the basic fundamentals of Linear Algebra. Included are the systems of linear equations, and matrices. Vectors in 2-space and 3-space lead to a study of vector spaces, linear transformation, eigenvalues, and eigenvectors. 

Note Fall semester only.

Prerequisite MATH 221.

A. Solve systems of linear equations using Gaussian elimination.

B. Solve systems of homogeneous linear equations.

C. Perform matrix operations.

D. Define elementary matrices and use them to find A-1.

E. Solve the equation AX=B using matrices.

F. Evaluate determinants.

G. Solve systems of linear equations using Cramer’s rule.

H. Perform operations on vectors in 2-space and 3-space.

I. Use Euclidean n-space to develop general vector spaces.

J. Use the definition to determine if functions are subspaces of a vector space.

K. Use the definition to determine if sets of vectors are linearly independent.

L. Determine if sets of vectors form a basis and calculate the dimension.

M. Determine the row and column rank of a matrix.

N. Define linear transformations and examine some examples.

O. Use properties of linear transformations from RN to RM to find the kernel and range

P. Evaluate Eigenvalues and Eigenvectors.

Q. Diagonalize the square matrix A using P-1AP.

Content
A. Systems of linear equations

B. Gaussian and Gauss-Jordan elimination

C. Matrices and matrix operations

D. The determinant

E. Cramer’s Rule

F. Vectors in 2-space and 3-space

G. Vector spaces

H. Eigenvalues and Eigenvectors

I. Linear transformations

Student Evaluation
Periodic examinations, daily assignments, and a final examination.