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Analytical Geometry \& Linear Algebra -- II
- Course name: Analytical Geometry \& Linear Algebra -- II
- Course number: XYZ
Course Characteristics
Key concepts of the class
- fundamental principles of linear algebra,
\item concepts of linear algebra objects and their representation in vector-matrix form
\end{itemize}
What is the purpose of this course?
Course objectives based on Bloom’s taxonomy
- What should a student remember at the end of the course?
By the end of the course, the students should be able to
- List basic notions of linear algebra
\item Understand key principles involved in solution of linear equation systems and the properties of matrices \item Linear regression analysis \item Fast Fourier Transform \item How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
- What should a student be able to understand at the end of the course?
By the end of the course, the students should be able to
- Key principles involved in solution of linear equation systems and the properties of matrices
\item Become familiar with the four fundamental subspaces \item Linear regression analysis \item Fast Fourier Transform \item How to find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
- What should a student be able to apply at the end of the course?
By the end of the course, the students should be able to
- Linear equation system solving by using the vector-matrix approach
\item Make linear regression analysis \item Fast Fourier Transform \item To find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition
Course evaluation
Type | Points |
---|---|
Labs/seminar classes | 20 |
Interim performance assessment | 30 |
Exams | 50 |
Grades range
Grade | Points |
---|---|
A | [85, 100] |
B | [65, 84] |
C | [50, 64] |
D | [0, 49] |
Resources and reference material
- Gilbert Strang. Linear Algebra and Its
Applications, 4th Edition, Brooks Cole, 2006. ISBN: 9780030105678 \item Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714
\end{itemize}
\paragraph{Reference material:} \begin{itemize}
\item Gilbert Strang, Brett Coonley, Andrew Bulman-Fleming. Student Solutions Manual for Strang's Linear Algebra and Its Applications, 4th Edition, Thomson Brooks, 2005. ISBN-13: 9780495013259
\end{itemize}
Course Sections
The main sections of the course and approximate hour distribution between them is as follows:
Section 1
Section title
Linear equation system solving by using the vector-matrix approach
Topics covered in this section
- The geometry of linear equations. Elimination with matrices.
\item Matrix operations, including inverses. and factorization. \item Transposes and permutations. Vector spaces and subspaces. \item The null space: Solving and . Row reduced echelon form. Matrix rank.
\end{itemize}
What forms of evaluation were used to test students’ performance in this section?
Form | Yes/No |
---|---|
Development of individual parts of software product code | 1 |
Homework and group projects | 1 |
Midterm evaluation | 1 |
Testing (written or computer based) | 1 |
Reports | 0 |
Essays | 0 |
Oral polls | 0 |
Discussions | 1 |
Typical questions for ongoing performance evaluation within this section
- How to perform Gauss elimination?
\item How to perform matrices multiplication? \item How to perform LU factorization? \item How to find complete solution for any linear equation system Ax=b?
Typical questions for seminar classes (labs) within this section
- Find the solution for the given linear equation system by using Gauss elimination.
\item Perform factorization for the given matrix . \item Factor the given symmetric matrix into with the diagonal pivot matrix . \item Find inverse matrix for the given matrix .
Tasks for midterm assessment within this section
Test questions for final assessment in this section
- Find linear independent vectors (exclude dependent): , , , , . Find if is a composition of this vectors. Find .
\item Find : ( – upper-triangular matrix). Find , if . \item Find complete solution for the system , if and . Provide an example of vector b that makes this system unsolvable.