Revision as of 16:13, 6 December 2021

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,
concepts of linear algebra objects and their representation in vector-matrix form

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
Understand key principles involved in solution of linear equation systems and the properties of matrices
Linear regression analysis
Fast Fourier Transform
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
Become familiar with the four fundamental subspaces
Linear regression analysis
Fast Fourier Transform
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
Make linear regression analysis
Fast Fourier Transform
To find eigenvalues and eigenvectors for matrix diagonalization and single value decomposition

Course evaluation

Course grade breakdown
Type	Points
Labs/seminar classes	20
Interim performance assessment	30
Exams	50

Grades range

Course grading 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

Gilbert Strang. Introduction to Linear Algebra, 4th Edition, Wellesley, MA: Wellesley-Cambridge Press, 2009. ISBN: 9780980232714

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.
Matrix operations, including inverses. $LU$ and $LDU$ factorization.
Transposes and permutations. Vector spaces and subspaces.
The null space: Solving $Ax=0$ and $Ax=b$ . Row reduced echelon form. Matrix rank.

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?
How to perform matrices multiplication?
How to perform LU factorization?
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 $Ax=b$ by using Gauss elimination.
Perform $A=LU$ factorization for the given matrix $A$ .
Factor the given symmetric matrix $A$ into $A=LDL^{T}$ with the diagonal pivot matrix $D$ .
Find inverse matrix $A^{-}1$ for the given matrix $A$ .

Tasks for midterm assessment within this section

Test questions for final assessment in this section

Find linear independent vectors (exclude dependent): ${\overrightarrow {a}}=[4,0,3,2]^{T}$ , ${\overrightarrow {b}}=[1,-7,4,5]^{T}$ , ${\overrightarrow {c}}=[7,1,5,3]^{T}$ , ${\overrightarrow {d}}=[-5,-3,-3,-1]^{T}$ , ${\overrightarrow {e}}=[1,-5,2,3]^{T}$ . Find $rank(A)$ if $A$ is a composition of this vectors. Find $rank(A^{T})$ .
Find $E$ : $EA=U$ ( $U$ – upper-triangular matrix). Find $L=E^{-}1$ , if

     $A=\left({\begin{array}{ccc}2&5&7\\6&4&9\\4&1&8\\\end{array}}\right)$ .

Find complete solution for the system $Ax=b$ , if $b=[7,18,5]^{T}$ and

    $A=\left({\begin{array}{cccc}6&-2&1&-4\\4&2&14&-31\\2&-1&3&-7\\\end{array}}\right)$ .
      Provide an example of vector b that makes this system unsolvable.

@@ Line 68: / Line 68: @@
 == 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.
+* Matrix operations, including inverses. <math>LU</math> and <math>LDU</math> factorization.
+* Transposes and permutations. Vector spaces and subspaces.
+* The null space: Solving <math>Ax = 0</math> and <math>Ax = b</math>. Row reduced echelon form. Matrix rank.
+==== What forms of evaluation were used to test students’ performance in this section? ====
+{| class="wikitable"
+|+
+|-
+! 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?
+# How to perform matrices multiplication?
+# How to perform LU factorization?
+# 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 <math>Ax=b</math> by using Gauss elimination.
+# Perform <math>A=LU</math> factorization for the given matrix <math>A</math>.
+# Factor the given symmetric matrix  <math>A</math> into  <math>A=LDL^T</math> with the diagonal pivot matrix <math>D</math>.
+# Find inverse matrix <math>A^-1</math> for the given matrix <math>A</math>.
+==== Tasks for midterm assessment within this section ====
+==== Test questions for final assessment in this section ====
+# Find linear independent vectors (exclude dependent): <math>\overrightarrow{a}=[4,0,3,2]^T</math>, <math>\overrightarrow{b}=[1,-7,4,5]^T</math>, <math>\overrightarrow{c}=[7,1,5,3]^T</math>, <math>\overrightarrow{d}=[-5,-3,-3,-1]^T</math>, <math>\overrightarrow{e}=[1,-5,2,3]^T</math>. Find <math>rank(A)</math> if <math>A</math> is a composition of this vectors. Find <math>rank(A^T)</math>.
+# Find <math>E</math>: <math>EA=U</math> (<math>U</math> – upper-triangular matrix). Find <math>L=E^-1</math>, if
+     <math>A=\left(
+         \begin{array}{ccc}
+& 5 & 7 \\
+& 4 & 9 \\
+& 1 & 8 \\
+         \end{array}
+       \right)</math>.
+# Find complete solution for the system <math>Ax=b</math>, if <math>b=[7,18,5]^T</math> and
+    <math>A=\left(
+         \begin{array}{cccc}
+& -2 & 1 & -4 \\
+& 2 & 14 & -31 \\
+& -1 & 3 & -7 \\
+         \end{array}
+       \right)</math>.
+       Provide an example of vector b that makes this system unsolvable.

Difference between revisions of "IU:TestPage"

Revision as of 16:13, 6 December 2021

Contents

Analytical Geometry \& Linear Algebra -- II

Course Characteristics

Key concepts of the class

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?

- What should a student be able to understand at the end of the course?

- What should a student be able to apply at the end of the course?

Course evaluation

Grades range

Resources and reference material

Course Sections

Section 1

Section title

Topics covered in this section

What forms of evaluation were used to test students’ performance in this section?

Typical questions for ongoing performance evaluation within this section

Typical questions for seminar classes (labs) within this section

Tasks for midterm assessment within this section

Test questions for final assessment in this section

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