Linear Algebra

Course title 

4042402-4

Course code 

4

Level

Lecture : 4

Lab        : --

Credit    : 4

Hours

4800141-4 Introduction to Mathematics II

Pre-requisites

• 404-354-3 Discrete MathematicsMath

• 404-342-3 Introduction of Rings theory Math

Co-requisites

The main purpose of this course are:

1-Linear equations in linear algebra: systems of linear equations, consistent and inconsistent systems of linear equations, examples

2-Elementary row operations, row reduction and echelon forms: examples

3-Matrix Algebra: Matrix operations,  Properties of matrix multiplication,

the inverse of a matrix (invertible matrix theorem), elementary matrices, column space and null space of a matrix: examples

4-Determinants: Recursive definition of a determent, properties of determinants.  Applications: Cramer's rule and volume.

5-Vector spaces: Definition, examples, substructures, and linear transformations of vector spaces examples

6-Linearly independence and basis of a vector space: examples

7-Eigen values and Eigenvectors of matrices , Orthogonality and least Squares.

Objectives

• Linear equations in linear algebra: systems of linear equations, consistent and inconsistent systems of linear equations, examples

• Elementary row operations, row reduction and echelon forms: examples

• Matrix Algebra: Matrix operations, Properties of matrix multiplication, the inverse of a matrix (invertible matrix theorem), elementary matrices, column space and null space of a matrix: examples

• Determinants: Recursive definition of a determent, properties of determinants. Applications: Cramer's rule and volume.

• Vector spaces: Definition, examples, substructures, and linear transformations of vector spaces examples

• Linearly independence and basis of a vector space: examples

• Eigen values and Eigenvectors of matrices , Orthogonality and least Squares

Description