MATB 253 – LINEAR ALGEBRA

COURSE OUTLINE AND ASSESSMENT POLICY

Lecturer : Zarina Abdul Rahman Semester 3 : 28 May – 30Aug 2012

Office : BN-1-039 E-mail : zarina@uniten.edu.my

Consultation hours: Mon , Thurs 3 - 4 pm

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Course Objectives :

Students who have completed this course are expected to be able to:

1. solve systems of linear equations using the Gaussian/ Gauss-Jordan elimination, Cramer’s rule and the inverse of a matrix,

2. evaluate determinants using row reduction and cofactor expansion, 3. find the standard matrix of linear transformations from n-space to m-space, 4. test for subspace of a vector space and find the spanning set for the vector

space,5. show whether a set of vectors is a basis and determine the dimension of a vector

space6. find a basis for the row space, column space and nullspace of a matrix7. calculate the rank and nullity of a matrix8. use the Gram- Schmidt process to orthonormal bases for inner product spaces,9. find the eigenvalues and the corresponding eigenvectors of a square matrix and

hence determine whether the matrix is diagonalizable,10. apply some concepts of linear algebra to Electrical Networks, Graph Theory,

and Cryptography.

Course Description :

Students should be able to solve systems of linear equations using the Gaussian/ Gauss-Jordan elimination, Cramer’s rule and the inverse of a matrix, calculate the determinants, find the standard matrix of linear transformations from Rn to Rm, determine whether a set of objects together with operations defined on it form a vector space, test for a subspace, show whether a set of vectors is a basis, determine the dimension of a vector space, find a basis for the row space, column space and nullspace of a matrix, calculate the rank and nullity of a matrix, give examples of inner product spaces, use the Gram- Schmidt process to find an orthonormal basis, find the eigenvalues and the corresponding eigenvectors of a square matrix, how to diagonalize a matrix. Some applications of linear algebra to engineering are discussed.

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Evaluation and Percentage Weightage:

Weightages Dates DurationAssignmnets 10% -Quizzes 10% 1 hourMid-Sem Test 30% 20/07/2012

(5 pm)1 ½ hour

Final Comprehensive Exam

50% Formal 2 hr. 30 mins.

Total 100%

Academic Rules on Attendance (From ‘PERATURAN AKADEMIK SARJANA MUDA’, Uniten)

Clause 8.1 A Student must attend at least 80% of the total number of class meetings (lecture and tutorial) that have been scheduled for the course.

Clause 8.2 A student whose attendance is less than 80% of the total number of class meetings without reasons acceptable to the College/Central Dean, may be barred from attending subsequent classes or sitting for any assessment from then on.

Course Outline

TOPICSChapter 1 SYSTEMS OF LINEAR EQUATIONS AND MATRICES

1.1 Introduction to Systems of Linear Equations1.2 Gaussian Elimination1.3 Matrices and Matrix Operations1.4 Inverses; Rules of Matrix Arithmetic 1.5 Elementary Matrices and a Method for Finding 1.6 Further Results on Systems of Equations and Invertibility1.7 Diagonal, Triangular, and Symmetric Matrices.

Chapter 2 DETERMINANTS

2.1 Determinants by Cofactor Expansion2.2 Evaluating Determinants by Row Reduction2.3 Properties of the Determinant Function2.4 A Combinatorial Approach to Determinants

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Chapter 4 EUCLIDEAN VECTOR SPACES

4.1 Euclidean n-Space4.2 Linear Transformations from Rn to Rm

4.3 Properties of Linear Transformations from Rn to Rm .

Chapter 5 GENERAL VECTOR SPACES

5.1 Real Vector Spaces5.2 Subspaces5.3 Linear Independence5.4 Basis and Dimension5.5 Row Space, Column Space and Nullspace5.6 Rank and Nullity

Chapter 6 INNER PRODUCT SPACES

6.1 Inner Products6.2 Angle and Orthogonality in Inner Product Spaces6.3 Orthonormal Bases ; Gram- Schmidt Process

Chapter 7 EIGENVALUES, EIGENVECTORS

7.1 Eigenvalues and Eigenvectors 7.2 Diagonalization

Chapter 11 APPLICATIONS OF LINEAR ALGEBRA

11.2 Electrical Networks11.7 Graph Theory11.16 Cryptography

Reference Book : Anton H. and Rorres C., Elementary Linear Algebra (Applications Version), 9th Edition, John Wiley & Sons, Inc, 2005.

NOTE : ALL MATERIALS AND ANNOUNCEMENT REGARDING THIS SUBJECT WILL BE POSTED ON MOODLE. HTTP://MOODLE.UNITEN.EDU.MYENROLMENT KEY: HIBISCUS

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Course Outcomes :

Course Outcomes PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11

1. solve systems of linear equations using the Gaussian/ Gauss-Jordan elimination, Cramer’s rule and the inverse of a matrix,

X

2. evaluate determinants using row reduction and cofactor expansion

X

3. find the inverse of a matrix by its adjoint or Gauss-Jordan elimination.

X

4. find the standard matrix of any linear transformations from n-space to m-space,

X

5. test for a subspace of any vector space and determine the spanning set for the vector space,

X

6. find a basis for the vector space and the fundamental matrix spaces

X

7. use the Gram- Schmidt process to find an orthonormal basis for an inner product space,

X

8. find the eigen values and the corresponding eigenvectors to diagonalize a square matrix.

X

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9. apply some concepts of linear algebra to Electrical Networks, Graph Theory, and Crytography.

X

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Assessment-Course Outcomes MatrixPO1 PO1 PO1 PO1 PO1 PO1 PO1 PO1 PO1

Assessments CO1 CO2 CO3 CO4 CO5 CO6 CO7 CO8 CO9Mid-Sem Test X X X XAssignment X X X X XQuizzes X X XFinal Exam X X X X X X X X X

PO Emphasis (%)PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 Total

Current Coverage(%)

100 100

Bloom's Coverage (%)Cognitive Psychomotor AffectiveLow Med High Total

Current Coverage(%) 20 70 10 100

What is Program Educational Objectives (PEO)? PEO are objectives that UNITEN graduates should achieve after five (5) years of graduation.

What are Programme Outcomes (PO)? PO are the expected traits that UNITEN students should have upon graduation.

Summary of BEEE and BEPE Programme Educational Objectives (PEO)

PEO No.

Program Educational Objectives

UNITEN produces EE and EP engineering graduates who:PEO1Are practicing engineers in electrical engineering with the ability to venture into other related fields.

PEO2Hold senior engineering positions and/or establish their own enterprises.

PEO3Have professional qualifications/certifications in electrical engineering related areas.

PEO4Are actively engaged in electrical engineering activities, in specialized areas such as electronics design, communications, control and instrumentation, power generation, power transmission and power distribution.

BEEE and BEPE Programme Outcomes (PO)

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PO No.

Program Outcomes

Students graduating from the Bachelor of Electrical & Electronics Engineering (BEEE) and Bachelor of Electrical Power Engineering (BEPE) programmes will have the ability to:

PO1 Acquire and understand fundamental knowledge of mathematics, science and electrical engineering principles

PO2 Apply engineering principles in solving problems relevant to electrical engineering

PO3 Analyze electrical engineering related problems

PO4 Apply critical thinking in designing and evaluating components, processes and systems related to electrical engineering

PO5 Comprehend the principles of sustainable development

PO6 Comprehend professional and ethical responsibilities

PO7 Apply engineering tools and techniques to conduct engineering design/experiments as well as to analyse data

PO8 Communicate effectively

PO9 Function effectively as a team member as well as a leader

PO10 Appreciate the social, cultural, global and environmental responsibilities of a professional engineer with awareness of contemporary issues

PO11 Acknowledge the need for, and be able to engage in life-long learning

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