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 TI86 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 preengineering option and is recommended as an
elective for
students who select from the fol lowing 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 ope rations to find the inverse of a matrix.
4. To evaluate determinants.
5. To use properties of de terminants 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 GramSchmidt process.
16. To understand linear transformations and to perform them.
17. To construct the matrices of linear transformations.
18. To find the eigen values 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 100 points
100 points
100 points
100 points
100 points 
13 45
9, 11, 12, 13, 14
5, 6, 7, 8, 15
16, 17
120 
FINAL GRADING PLAN
Based Upon Percentages
A = 90100
B = 8089
C = 7079
D = 6069
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 As signments /
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 


13

Test 1 (Chapter 1 and
Chapter 2 sections 13) 



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.

45

Test 2 (Chapter 2 Sections 4 & 5
and Chapter 3) 



Vectores in R^{n} 
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 R^{n} 
Exercises 5.1 




X. 
6 
Inner Product Spaces 
Exercises 5.2 

15

Othonormal Bases; GramSchmidt
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. 
120 
Final Exam 

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