Syllabus for Elements of Linear Algebra

Catalog Description:
This course is a study of matrices, systems of linear equations ,
determinants, vectors, vector spaces, eigenvalues, eigenvectors,
and other selected topics.

Credit Hours: 3 sem hrs
Contact Hours: 3 hrs/wk
Lab Hours: 0

Prerequisite(s): MATH 1910

Required Elementary

Text(s):

Linear Algebra
Title

Howard Anton
Author(s)

9th/2005
Edition/Date

John Wiley & Sons
Publisher

Required Supplies/Material(s):

Graphics Calculator --TI-86 is preferred, but any
calculator which will perform matrix operations
will be acceptable

Recommended Supplementary Material(s):

Student Group for Whom Course is Required/Intended:
This course is required for
students selecting pre -engineering option and is recommended as an elective for
students who select from the following options: computer science, mathematics, and
physics.

GOALS

The goals of instruction of MATH 2010 are :
1. to teach the skills needed to solve systems of equations using various matrix methods,
2. to teach skills needed to evaluate determinants,
3. to teach the skills necessary to use vectors in other areas,
4. to teach the student how to change bases and construct orthogonal bases,
5. to teach the skills necessary to perform linear transformations ,
6. to teach the student how to find eigenvectors, and
7. to make the student familiar with certain applications of matrix
theory.

OBJECTIVES

Through the study of MATH 2010, the student should be able to do the following.
1. Solve systems of linear equations using Gaussian elimination.
2. To perform matrix operations.
3. To use matrix operations to find the inverse of a matrix.
4. To evaluate determinants.
5. To use properties of determinants to solve problems.
6. To find the norm of a vector and do vector arithmetic .
7. To find dot products.
8. To find the cross product of two vectors .
9. To do vector operations in N-dimensional space.
10. To study orthogonality of a matrix and vectors.
11. To understand and use general vector spaces, subspaces, and spanning sets.
12. To find the dimension and basis of a vector space.
13. To determine the linear independence or dependence of sets of vectors.
14. To determine the rank of a matrix and the uses of the rank.
15. To construct an orthonormal basis using the Gram-Schmidt process.
16. To understand linear transformations and to perform them.
17. To construct the matrices of linear transformations.
18. To find the eigenvalues and eigenvectors of certain matrices.
19. To diagonalize matrices.
20. To do orthogonal diagonalizations.

SUGGESTED EVALUATION PLAN

TASK

WEIGHT

OBJECTIVES

Test 1

Test 2

Test 3

Test 4

Test 5

Test 6 - Final Exam

100 points

1-3

4-5

9, 11, 12, 13, 14

5, 6, 7, 8, 15

16, 17

1-20

FINAL GRADING PLAN
Based Upon Percentages

A = 90-100
B = 80-89
C = 70-79
D = 60-69
F = Below 60

Additional Comments :

INSTRUCTIONAL SCHEDULE
for
MATH 2010 - Elements of Linear Algebra
Course Number and Name

Week	Objective Numbers	Content to be Covered	Student Assignments/ Supplementary Material(s)
I.	1	Introduction to Systems of Linear Equations	Exercises 1.1
	1	Gaussian Elimination and Gauss - Jordan Elimination	Exercises 1.2
	1	Applications of Systems of Linear Equations	Exercises 1.3

II.	2	Operations with Matrices	Exercises 2.1
	2	Properties of Matrix Operations	Exercises 2.2
	2	The Inverse of a Matric	Exercises 2.3

III.		Review for Test
	1-3	Test 1 (Chapter 1 and Chapter 2 sections 1-3)
		Elementary Matrices	Exercises 2.4

IV.	4	Applications of Matrix Operations	Exercises 2.5
		The Determinant of a Matrix	Exercises 3.1
	4	Evaluating of a Determinant Using Elementary Operations	Exercises 3.2

V.	5	Properties of Determinant	Exercises 3.3
		Applications of Determinants	Exercises 3.4
		Review for Test 2	Review

VI.	4-5	Test 2 (Chapter 2 Sections 4 & 5 and Chapter 3)
		Vectores in Rⁿ	Exercises 4.1
		Vector Spaces	Exercises 4.2

VII.	11	Subspaces of Vector Spaces	Exercises 4.3
	11, 13	Spanning Sets and Linear Independence	Exercises 4.4
	12	Basic and Dimension	Exercises 4.5

VIII.	14	Rank of a Matrix and Systems of Linear Equations	Exercises 4.6
		Coordinates and Change of Basis	Exercises 4.7
		Applications of Vector Spaces	Exercises 4.8

IX.		Review for Test 3
	9,11,12, 13,14	Test 3 (Chapter 4)
	5, 6, 7	Length and Dot product in Rⁿ	Exercises 5.1

X.	6	Inner Product Spaces	Exercises 5.2
	15	Othonormal Bases; Gram-Schmidt Process	Exercises 5.3
	8	Applications of Inner Product Spaces	Exercises 5.5

XI.		Review for Test 4
	5,6,7,8, 15	Test 4 (Ch. 5 Sections 1,2,3,5)
		Introductions to Linear	Exercises 6.1
	16	Transformations

XII.	16	The Kennel and Range of a Linear Transformation	Exercises 6.2
	17	Matrices for Linear Transformation	Exercises 6.3
		Transitions Matrices and Similarity	Exercises 6.4

XIII.		Applications of Linear Transformations	Exercises 6.5
		Review for Test 5
	16,17	Test 5 (Chapter 6)

IV.	18	Eigenvalues and Eigenvectors	Exercises 7.1
	19	Diagonalization	Exercises 7.2
	10, 20	Symmetric Matrices and Orthogonal Diagonalization;	Exercises 7.3

XV.		Induction	Appendix A - Induction
		Review for final

XVI.	1-20	Final Exam

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