# Linear Algebra

### 1. Course Description:

This is a first course in linear algebra. It is a 3 credit single semester course with four contact hours a week. It is mainly designed for statistics and computer students. This course introduces the students to the many topics including systems of linear equations, matrices, determinants, vector spaces, eigenvalues and eigenvectors and linear transformations. The prerequisite of this course is Calculus I.

### 2. Course Contents:

Systems of Linear Equations:

Introduction to systems of linear equations. Row operations. Gaussian eliminations. Gauss-Jordan eliminations. Homogeneous linear systems.

Matrices and Matrix Operations:

Elementary matrices. The inverse of a matrix. Existence of the inverse. The inverse as a product of elementary matrices. The inverse via row operations.

Determinants:

Definition and properties. The existence of the inverse of a matrix. The minor, cofactor and adjoint. Cramer’s rule.

Vector Spaces:

Vector spaces. Sub vector spaces. Linear independence and linear dependence. The spanning set of a vector space. Basis. Dimension. Row space. Column space. Null space. Rank of a matrix. Nullity of a matrix.

Linear Transformations:

Linear transformation. Kernel. Range. Inverse of a linear transformation. Existence of the inverse transformation. Determining the rule of the inverse. Linear transformations and matrices.

Eigenvalues and Eigenvectors:

The transition matrix from a basis to another. Eigenvalues, and Eigenvectors. Diagonalization.

Applications.

### 3. Course Objectives:

To introduce systems of linear equations and discuss methods to solve them.

To introduce matrices and their properties.

To acquaint students with determinants and their properties and applications.

To familiarize students with vector spaces.