MM105 : Linear Algebra 1

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

03

Prerequisite

Overview

This course introduces students to the basic concepts of matrices and concepts related to determinants. It also deals with ways to solve a system of linear equations using determinants. This course aims to develop the student's ability to identify types of matrices and perform row operations on matrices, as well as knowing ways to find the inverse of a matrix and determine whether it is invertible. The course also aims to enhance students' skills in finding a solution to a system of linear equations using matrices and determinants, through scheduled training and a variety of evaluation methods.

The course focuses on using matrices and determinants to solve a system of linear equations.

Intended learning outcomes

By the end of the course, the student should be able to:

1. Explain the basic concepts of arrays, their types and operations.
2. Distinguish row operations on matrices and scalar and reduced matrices
3. Explain many ways to find the inverse of a matrix.
4. Show how to use matrices to solve linear equations
5. Describe determinants and their use in finding the inverse of a square matrix
6. The solution of the system defines linear equations using determinants
7. Explain the terms vector space and subspace.
8. Explain the basic concepts of arrays, their types and operations
9. Discusse row operations on matrices and scalar and reduced matrices
10. Analyze methods for finding the inverse of a matrix
11. Infer and evaluate the solution of systems of linear equations using matrices
12. Classify determinants and use them to find the inverse of a square matrix
13. Proposes and analyzes ways to solve the system of linear equations using determinants
14. Check the conditions for a vector space as well as a subspace
15. Solve a number of exercises and problems with more than one idea about matrices, their types, and operations on them
16. Applie exercises and problems on the matrix and its inverse and the determinants
17. Provide solutions to new and different problems and multiple determinants
18. It Applies the row and reduced matrix to solve systems of linear equations
19. There is a solution to systems of linear equations. using selectors
20. Employ knowledge of vector space terms in proving some issues
21. Prove whether space is a vector and a subspace.

Teaching and learning methods

1. Practical and theoretical lectures.
2. Discussion and dialogue
3. Brainstorm
4. Working papers, case study
5. Presentations
6. Videos and e-learning
7. Using software and computer applications such as ( MATLAB), geogebra, geometer).
8. Intensifying applications, solving problems, and linking ideas to reality and life situations

Methods of assessments

1. A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor.
2. Short tests (written or oral), demonstration tasks, applications, exercises, and presentation = 15 marks or left to the course instructor
3. Written final exam (essay + objective) = 60 marks

Course contents

the week	Scientific subject	The number of hours	lecture	Lab	exercises
1	Matrices and operations defined on them: Algebraic properties of operations on matrices.	3	2	-	1
2	Special types of arrays.	3	2	-	1
3	Matrix pivot, prime matrices, equivalent matrices.	3	2	-	1
4	Row operations on matrices, scalar and reduced matrices.	3	2	-	1
5	First midterm exam (2 hours)
5	Matrix inverse and its properties.	1	1	-	
6	Use elementary operations to calculate the inverse of a matrix.	3	2	-	1
7	Determinants: definition, how to find them, properties.	3	2	-	1
8	Use determinants to find the inverse of a matrix.	3	2	-	1
9	System of linear equations: definition, general concepts, methods to find their solution using matrices.	3	2	-	1
10	Second midterm exam (two hours)
10 -11	Methods for solving system linear equations using determinants.	4	3	-	1
12	Vector Spaces: A Review of Vectors	3	2	-	1
13	Definition of vector space, operations defined on vector space.	3	2	-	1
14	Subspaces, linear independence and linear correlation, basis and dimension.	3	2	-	1
15-16	final exam
	the total	42

Reference

References address	publisher	Release	Author	where it is located
Fundamentals of Linear Algebra	The new book	2002	Dr. Mabrouk Yunus

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