Semester:

2

Course Code:

EM1020

Course Name:

Linear Algebra

Credit Value:

3 (Notional hours: 150)

Prerequisites:

None

Core/Optional

Core

Hourly Breakdown

Lecture hrs.

Tutorial hrs.

Assignment hrs.

Independent Learning & Assessment hrs.

35

10

-

105

Course Aim: To encourage students to develop a working knowledge of the central ideas of linear algebra: vector spaces, linear transformations, orthogonality, eigenvalues, eigenvectors and canonical forms and the applications of these ideas in science and engineering.

Intended Learning Outcomes:

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

➢    apply the knowledge of matrices, Gaussian reduction and determinants to solve systems of linear equations.

➢    apply the properties of vector spaces and to generalize the concepts of Euclidean geometry to arbitrary vector spaces.

➢    identify linear transformations, represent them in terms of matrices, and interpret their geometric aspects.

➢    calculate eigenvalues and Eigenvectors of matrices and linear transformations and apply the concepts in physical situations.

➢    prove eigenvalue properties of real symmetric matrices and apply them in quadratic forms.

Course Content:

➢    Matrix Algebra: Operations, elementary matrices, inverse, partitioned matrices.

➢    Determinants: Introduction and properties.

➢    Vector spaces: Definition, subspaces, linear independence and spanning, basis, change of basis, normed spaces, inner product spaces, Gram-Schmidt orthonormalization.

➢    Linear Transformations: Introduction, matrix representation, operations of linear transformations, change of basis.

➢    System of linear equations: Gauss and Jordan elimination; LU factorization, least square approximations, ill-conditioned and overdetermined systems.

➢    Characteristic value problem: Computing eigenvalues and eigenvectors, Eigen-basis, diagonalization, matrix exponentials.

➢    Real Symmetric matrices: Properties, definiteness, quadratic forms, applications.

Teaching /Learning Methods:

Classroom lectures, tutorial discussions and in-class assignments

Assessment Strategy:

Continuous Assessment
50%

Final Assessment
50%

Details:
Tutorials/Assignments/Quizzes 20%
Mid Semester Examination 30%

Theory (%)

50%

Practical (%)

 -

Other (%)

 -

Recommended Reading:

➢    Gilbert Strang, Introduction to Linear Algebra, 5th edition, (2010), Cambridge Press.

➢    David C. Lay, S. R. Lay & J. Mcdonald, Linear Algebra and its Applications, 5th edition, (2012), Pearson.

➢    David Poole, Linear Algebra: A Modern introduction, 4th edition, (2005), Cengage.

➢    Thomas. S. Shores, Applied Linear Algebra and Matrix Analysis, (2007), Springer.