BMTS310-2026

BMTS310
Matrix Theory

ECTS Value: 6 ECTS

Contact Hours: 30

Self Study Hours: 72

Assessment Hours: 48

Overall Objectives and Outcomes

The study unit on matrix theory aims to help course participants comprehend that matrices are rectangular arrays of values, symbols, or expressions arranged in rows and columns. This module introduces different matrix operations of addition, multiplication by scalar and matrix multiplication. Determinants and inverse are also introduced to solve simultaneous equations using matrix inverse and Cramer’s rule. Additionally, the Gauss-Jordan elimination (elementary row operations) is used to determine the solution of a system of linear equations with 3 unknowns and give an interpretation of the result. The Jacobi iterative method is also used to determine the solution of a diagonally dominant system of linear equations with 3 and 4 unknowns. At the end of the study unit, the matrix operator of transformations in 2D and 3D space is found. Transformation matrices are combined, repeated and used to find the image given the object or the object given the image of a transformation. This module offers strong frameworks and methods for transforming, and evaluating data in theoretical and practical contexts, and solving systems of linear equations. The results of this module are reached through different worked examples and real-life applications. The course participants are encouraged to work out additional examples to strengthen their knowledge of matrix theory.

By the end of this module, the learner will be able to:

Competences

- a)Work out basic matrix operations and explain the key matrix properties accurately;
- b)Compute the determinant and inverses of matrices;
- c)Determine the solution of a system of linear equations with 3 unknowns by giving a geometric interpretation of the result;
- d)Use the iterative method to determine the solution of a diagonally dominant system of linear equations with 3 and 4 unknowns;
- e)Represent linear transformations using matrices and analyse the relationship between linear transformations and matrix operations to find the object and image.

Knowledge

- - a)Examine various matrix definitions as well as the addition, matrix multiplication, and multiplication by scalar matrix operations;
  - b)Provide a geometric interpretation of the findings in solving a system of linear equations with three unknowns that have a unique solution, linear dependence, or inconsistency. The Gauss-Jordan elimination method is also introduced;
  - c)Know and apply the theoretical aspects of matrices, including linear transformations and finding the image given the object or the object given the image of the transformation;
  - d)Determine the solution of a diagonally dominant system of linear equations with 3 or 4 unknowns using the Jacobi iterative method;
  - e)Find the image given the object or to find the object given the matrix standard transformation in 2D and 3D.

Skills

- - a)Critically analyse and solve complex problems involving matrices;
  - b)Solve simultaneous equations with three unknowns requiring the use of determinants and inverses;
  - c)Perform proficient detailed calculations and explain the underlying mathematical concepts;
  - d)Execute matrix operations (addition, subtraction, multiplication);
  - e)Calculate determinants and inverses with 3 unknowns using matrix inverse and Cramer’s rule;
  - f)Apply the matrix theory to solve and interpret the systems of linear equations having 3 unknowns using the Gauss-Jordan elimination;
  - g)Solve a diagonally dominant system of linear equations with three and four unknowns using the Jacobi iterative approach.

Assessment Methods

This module will be assessed through: Forum, Presentation