PMAT 11232: Matrix Algebra

Course code    :  PMAT 11232

Title                   :  Matrix Algebra

Pre-requisites   :  A/L Combined Mathematics

Learning Outcomes:

On successful completion of the course, the student should be able to;

1. demonstrate the knowledge in the fundamentals of matrix algebra
2. apply elementary row operations to a matrix to transform it into its row-echelon form and find the inverse
of a square matrix
3. develop system of linear equations and represent in matrix form and apply Gaussian and Gauss-Jordan
method to solve simultaneous equations
4. classify a system of linear equations into consistent (unique solution and infinitely many solutions) and
inconsistent systems
5. identify the determinant of a square matrix, evaluate determinant using co-factors and apply elementary
row and column operations to evaluate determinants
6. describe and apply Cramer’s rule to solve system of linear equations
7. develop system of linear equations related to real world problems
8. explain and compute eigenvectors and eigenvalues of a matrix.

Course Contents: 

Matrices: 

• Algebra of matrices, Special types of matrices, Transpose of a matrix, Symmetric and skew-symmetric matrices, Inverse of a square matrix; Elementary row and column operations, Elementary matrices and their properties, Inverse matrices using Elementary row and column operations, Properties of Inverse matrices

System of Linear Equations: 

• Matrix representation of System of Linear equations, Row echelon form of a matrix, Gaussian and Gauss-Jordan Elimination, Solutions of System of Equations, Applications of System of Linear Equations.

Determinant of a matrix: 

• Expansion by co-factors, Determinants of Triangular matrices, Evaluation of determinants by elementary row operations, Cramer’s rule, and other applications of determinants.

Eigenvalues and Eigenvectors: 

• Eigenvalues and eigenvectors of a matrix and their properties.

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on tutorials, tests and end of course examination.

Recommended Reading: 

1. Larson, R. & Falvo, D.C. (8th Ed., 2016). Elementary Linear Algebra, Brooks Cole.
2. Andrilli, S. & Hecker, D. (5th Ed., 2016). Elementary Linear Algebra, Elsevier Science.
3. DeFranza, J. & Gagliardi, D. (2015). Introduction to Linear Algebra with Applications, Waveland Press.
4. Lay, D.C., Lay, S.R. & McDonald, J.J. (5th Ed., 2015). Linear Algebra and Its Applications, Pearson
5. Anton, H. & Rorers, C. (2014). Elementary Linear Algebra Applications, Wiley.