MAT1102 LINEAR ALGEBRA I

This course is a foundation course that introduces learners to the basic mathematical concepts. It covers the topics such as Vector Spaces, Matrices, Solutions of Systems of Linear Equations, Properties of Vector spaces, Diagonalisation, and Linear Transformations.

Course Objectives
On successful completion of this course unit, the learners should be able to:

• Define a vector space, give various types of vector spaces including Euclidian n-space, the matrix space, the polynomial space and matrix space.
• Construct matrices of different order, work with matrices, find determinants and their applications  
• Construct augmented matrices for system of linear equations, solve systems of linear equations by Gaussian and Gauss-Jordan elimination, and Echelon form.
• State properties of vector spaces, determine linear dependence and independence, calculate the rank, basis, dimension and kernel.
• Carry out matrix diagonalisation by use of eigenvalues and eigenvectors.
• Define line transformations and give their properties, determine kernel and range of transformation, determine singularity and change of basis.

Expected Learning Outcomes
This course unit will at the end of it, make students able to:

• To discuss the basic competence in the concepts, principles, and procedures in elementary mathematics application to matrices and linear equations as well as mathematical symbolism and computation.
• To encourage orderliness, speed and accuracy in the presentation of mathematical expressions in linear systems.
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly.
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills.
• To build a strong foundation in mathematical presentation as preparation for subsequent courses in pure mathematics and other sciences.