# BDIC1014J Linear Algebra (Engineering)

Linear algebra, a branch of mathematics concerning vectors and linear mappings between vector spaces, is a fundamental course for college mathematics. In this module basic ideas of Linear Algebra will be introduced. Topics covered are: vectors in 2- and 3-dimensional space; dot product, vector product and scalar triple product; orthogonal projection; lines and planes in 3-dimensional space; systems of linear equations; elementary row operations and Gaussian elimination; matrices; matrix algebra; determinants; inverses of matrices; eigenvalue and eigenvectors; diagonalization of a matrix; quadratic forms; vector space; rank of a matrix.

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Curricular information is subject to change

Learning Outcomes:

Students are expected to achieve the following competence:
• Giving algebraic and geometrical representations for vectors
• Performing arithmetic with vectors;
• Using vectors to solve classical geometric problems;
• Manipulating dot and cross products, and using them to solve geometric problems;
• Solving systems of linear equations in terms of Gaussian elimination and Cramer’s rule;
• Performing matrix arithmetic;
• Calculating inverse of a matrix and a determinant;
• Solving eigenvalue problem for a matrix;
• Diagonalizing a matrix;
• Solving a quadratic form problem in terms of matrix diagonalization;
• Being able to identifying the rank of a matrix;
• Giving the space spanned by a number of vectors.

Indicative Module Content:

Teaching Plan

Week 1: Appendix: Revisit to high school mathematics: Set theory, summation and product notations, mathematical induction.
Definitions & properties of vectors.
Week 2: Definitions & properties of vectors, scalar multiplication, linear independence. Tutorial 1.
Week 3: Dot product (algebraic & geometric definitions), projection of vectors, two important inequalities, applications.
Week 4: Cross product (algebraic & geometric definitions), applications. Tutorial 2.
Week 5: Applications of vectors: equations of lines and planes, scalar triple product.
Week 6: Matrices and systems of linear equations, Gaussian elimination. Tutorial 3.
Week 7: Row echelon form, reduced echelon form, homogeneous systems.
Week 8: Revision for mid-term exam. Tutorial 4.
Week 9: Matrix algebra, elementary matrices, partitioned matrices, LU decomposition.
Week10: Determinant of a matrix, properties of determinants. Tutorial 5.
Week12: Definitions of eigenvalue and eigenvector of a matrix. Tutorial 6.
Week13: Diagonalization of matrix.
Week14: Quadratic forms, positive and negative definite matrices, rank of matrix. Tutorial 7.
Week15: Vector spaces and subspaces spanned by vectors.
Week16: Revision for final exam.

Remarks:
1. In each odd week there are two lectures; in each even week there is one lecture and one tutorial.
2. The chapter of vector spaces is only a brief review of the theory. Interested students are encouraged to read reference textbooks, and wait for future advanced courses on algebra theory.

Student Effort Hours:
Student Effort Type Hours
Lectures

64

Practical

66

Total

130

Approaches to Teaching and Learning:
Lecturing (face-to-face teaching) + tutorials + group project on open questions + oral defense in full English + close-book examinations.
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
Not applicable to this module.

Assessment Strategy
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: Midterm Exam.
90 minutes examination, at 1/2 of the semester.
Unspecified No Alternative linear conversion grade scale 40% No

20

Continuous Assessment: Attendence recording and tutorial participation. Throughout the Trimester n/a Pass/Fail Grade Scale No

5

Examination: Quiz.
30 minutes examination, at 1/4 of the semester.
Unspecified No Alternative linear conversion grade scale 40% No

10

Examination: Final Exam.
90 minutes of examination, at the end of the semester.
Unspecified No Alternative linear conversion grade scale 40% No

50

Group Project: Assignment.
Essay based on group work + Oral presentation.
1st round: Selection based on the submitted essays. Top 15% enter into 2nd round.
2nd round: Selection based on oral defense.

15

Carry forward of passed components
No

Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board