Course Teaching Plan

MAT 101

Linear Algebra I

An introductory course covering matrices, determinants, systems of linear equations, eigenvalues, eigenvectors, and linear transformations.

15 Weeks 3 Contact Hours Weekly 1-Hour Seminar 2-Hour Lecture
Course Information

Course Overview

Course Code MAT 101
Course Title Linear Algebra I
Duration 15 Weeks
Contact Hours 3 Hours Weekly

Course Description

This course introduces the basic principles of linear algebra, focusing on matrices, matrix operations, elementary row operations, determinants, matrix inverses, systems of linear equations, eigenvalues, eigenvectors, and linear transformations.

Students will develop computational and problem-solving skills necessary for applying linear algebraic methods to mathematical and practical problems.

Competencies

Learning Outcomes

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

1. Define matrices and identify different types of matrices.
2. Perform matrix addition, subtraction, scalar multiplication, and matrix multiplication.
3. Apply elementary row operations to simplify matrices.
4. Determine row echelon and reduced row echelon forms.
5. Calculate determinants and apply their properties.
6. Find matrix inverses using row operations and determinants.
7. Solve systems of linear equations using different methods.
8. Find eigenvalues and eigenvectors of suitable matrices.
9. Explain and represent linear transformations using matrices.
10. Apply change of basis, coordinate transformations, and rotation matrices.
Evaluation

Assessment Scheme

Student performance will be evaluated through coursework, an in-semester test, and a final examination.

Component
Description
Weight
Test
Written test covering Weeks 1–7
20%
Assignment
Exercises, problem sets, and coursework
20%
Final Examination
Comprehensive examination covering the course
60%
Total 100%
Course Schedule

Weekly Teaching Plan

Click any week to view the seminar and lecture details.

Normal weeks contain a 1-hour seminar and a 2-hour lecture. Week 8 is reserved for the 2-hour test.

Topic: Introduction to Matrices

Seminar — 1 Hour
  • Meaning and notation of matrices
  • Rows, columns, and matrix entries
  • Basic matrix identification exercises
Lecture — 2 Hours
  • Definition and notation of a matrix
  • Order or size of a matrix
  • Equality of matrices
  • Representation of data using matrices

Topic: Special Types of Matrices and Matrix Operations

Seminar — 1 Hour
  • Identification of special matrices
  • Matrix addition and subtraction
  • Scalar multiplication exercises
Lecture — 2 Hours
  • Row, column, square, and rectangular matrices
  • Zero, diagonal, identity, and triangular matrices
  • Symmetric matrices
  • Matrix addition, subtraction, and multiplication

Topic: Elementary Row Operations

Seminar — 1 Hour
  • Row interchange
  • Row scaling
  • Row replacement exercises
Lecture — 2 Hours
  • Definition of elementary row operations
  • Interchanging rows
  • Multiplying a row by a non-zero scalar
  • Adding a multiple of one row to another

Topic: Row Echelon Forms and Inverse by Row Operations

Seminar — 1 Hour
  • Identification of echelon forms
  • Matrix reduction exercises
  • Guided inverse calculations
Lecture — 2 Hours
  • Row echelon form
  • Reduced row echelon form
  • Pivot positions
  • Rank of a matrix
  • Inverse using augmented matrices

Topic: Introduction to Determinants

Seminar — 1 Hour
  • 2 × 2 determinant calculations
  • 3 × 3 determinant calculations
  • Expansion practice
Lecture — 2 Hours
  • Definition of a determinant
  • Determinants of 2 × 2 and 3 × 3 matrices
  • Minors and cofactors
  • Cofactor expansion

Topic: Properties and Evaluation of Determinants

Seminar — 1 Hour
  • Application of determinant properties
  • Simplification of determinant calculations
  • Row-operation exercises
Lecture — 2 Hours
  • Determinants of triangular matrices
  • Effect of row interchange
  • Effect of scalar multiplication
  • Effect of row replacement
  • Evaluation through row reduction

Topic: Inverse of a Matrix Using Determinants

Seminar — 1 Hour
  • Minors and cofactors
  • Adjoint matrix construction
  • Inverse calculation exercises
Lecture — 2 Hours
  • Singular and non-singular matrices
  • Adjoint and cofactor matrices
  • Inverse matrix formula
  • Conditions for matrix invertibility
Test preparation: Review Weeks 1–7 and complete revision exercises.

Topic: Test Covering Weeks 1–7

Preparation / Consultation
  • Clarification of difficult concepts
  • Test instructions
  • Brief academic consultation
Test Session — 2 Hours
  • Matrix concepts and operations
  • Elementary row operations
  • Row echelon forms
  • Matrix inverses
  • Determinants and their properties

Topic: Systems of Linear Equations

Seminar — 1 Hour
  • Writing systems in matrix form
  • Augmented matrix exercises
  • Simple elimination problems
Lecture — 2 Hours
  • Definition of linear systems
  • Consistent and inconsistent systems
  • Unique and infinitely many solutions
  • Homogeneous systems
  • Augmented matrices

Topic: Matrix Form and Gaussian Elimination

Seminar — 1 Hour
  • Conversion of equations to matrices
  • Row reduction of systems
  • Interpretation of solution sets
Lecture — 2 Hours
  • Matrix representation of systems
  • Gaussian elimination
  • Back substitution
  • Pivot and free variables
  • Geometric interpretation of solutions

Topic: Methods for Solving Linear Systems

Seminar — 1 Hour
  • Gauss-Jordan elimination practice
  • Inverse matrix method
  • Cramer’s rule exercises
Lecture — 2 Hours
  • Gauss-Jordan elimination
  • Inverse matrix method
  • Cramer’s rule
  • Comparison of solution methods
  • Applications of linear systems

Topic: Eigenvalues and Eigenvectors

Seminar — 1 Hour
  • Eigenvalue equation
  • Characteristic polynomial practice
  • Simple eigenvalue calculations
Lecture — 2 Hours
  • Definition of eigenvalues and eigenvectors
  • Eigenvalue equation
  • Characteristic matrix
  • Characteristic polynomial
  • Characteristic equation

Topic: Computing Eigenvectors

Seminar — 1 Hour
  • Finding eigenvectors
  • Solving homogeneous systems
  • Checking eigenvector solutions
Lecture — 2 Hours
  • Finding eigenvectors from eigenvalues
  • Solving (A − λI)x = 0
  • Eigenspaces
  • Geometric interpretation of eigenvectors

Topic: Linear Transformations and Coordinate Representations

Seminar — 1 Hour
  • Testing whether a mapping is linear
  • Finding kernels and ranges
  • Matrix representation exercises
Lecture — 2 Hours
  • Definition of linear transformations
  • Kernel and range
  • Inverse transformations
  • Matrices of transformations
  • Coordinate transformations
  • Change of basis
  • Rotation matrices and coordinate axes

Topic: Comprehensive Revision and Examination Preparation

Seminar — 1 Hour
  • Review of key definitions and formulas
  • Common examination errors
  • Student questions and clarification
  • Short revision exercises
Lecture — 2 Hours
  • Revision of matrices and determinants
  • Revision of inverses and row reduction
  • Revision of linear systems
  • Revision of eigenvalues and eigenvectors
  • Revision of linear transformations
  • Final examination preparation
This week is reserved for consolidation and final examination preparation.

Reading List

The following texts provide supporting material for the study of linear algebra and its applications.

  1. Kolman, B. (1984). Introductory Linear Algebra with Applications (4th ed.). MacMillan Publishing Co., New York.
  2. Anton, H. (1997). Elementary Linear Algebra. Prentice-Hall International, Inc., New Jersey.
  3. Apostol, T. (1997). Multi Variable Calculus and Linear Algebra (2nd ed.). John Wiley and Sons.
  4. Anton, H., & Rorres, C. (2010). Elementary Linear Algebra: Applications Version (10th ed.). John Wiley and Sons.