San Diego Mesa College
Class Information Sheet
Semester: Spring 2016( 1/25/16 – 5/21/16)
Instructor: Yohannes Truneh
Tel. (619)- 388-2388; Email: ytruneh@sdccd.edu
Office: MS215S
Subject area and course number: Mathematics 254
Course Title: Introduction to Linear Algebra
Unit: 3
CRN: 91702
Class meets: Mon.& Wed. 11:10am – 12:35 p.m. in Room MS422.
Text: Elementary Linear Algebra by Larson & Edwards; 7th ed.
CATALOG COURSE DESCRIPTION:
This course serves as an introduction to the theory and applications of elementary linear algebra, and is the
basis for most upper division courses in mathematics. The topics covered in this course include matrix
algebra, Gaussian Elimination, systems of equations, determinants, Euclidean and general vector spaces,
linear bases of vector spaces, the change of basis theorem, eigenvalues and eigenvectors, the rank and
nullity of matrices and of linear transformations, orthogonality and inner product spaces. This course is
intended for the transfer student planning to major in mathematics, physics, engineering, computer science,
operational research, economics, or other sciences.
Student learning outcomes(SLO)
1. Students will find the basis for the kernel of a linear transformation of a given matrix.
2. Students will be able to orthogonally diagonalize a 3X3 symmetric matrix.
3. Students will be able to find bases for three fundamental subspaces of a matrix(rorspace, colspace,
and nullspace).
STUDENT LEARNING Objectives:
Upon successful completion of the course the student will be able to:
1. Solve systems of linear equations using several algebraic methods.
2. Construct and apply special matrices, such as symmetric, skew-symmetric, diagonal, upper
triangular
or lower triangular matrices.
3. Perform a variety of algebraic matrix operations, including multiplication of matrices,
transposes, and
traces.
4. Calculate the inverse of a matrix using various methods, and perform application problems
involving the
inverse.
5. Compute the determinant of square matrices and use the determinant to determine invertibility.
6. Derive and apply algebraic properties of determinants.
7. Perform vector operations on vectors from Euclidean Vector Spaces including vectors from
R^n.
8. Compute the equations of lines and planes and write these in their corresponding vector forms.
9. Perform linear transformations in Euclidean vector spaces, including basic linear operators,
and
determine the standard matrix of the linear transformation.
10. Prove whether a given structure is a vector space and determine whether a given subset of a
vector
space is itself a vector space.
11. Determine if a set of vectors spans a space, and if such a set is linearly dependent or
independent.
12. Determine if a set of functions is linearly independent using various techniques including
calculating
the determinant of the Wronskian.
13. Solve for the basis and the dimension of a vector space.
14. Determine the rank, the nullity, the column space and the row space of a matrix.
15. Describe orthogonality between vectors in an abstract vector space by means of an inner
product, and
compute the inner product between vectors of a this inner product space.
16. Compute the QR-decomposition of a matrix using the Gram-Schmidt process.
17. Perform changes of bases for a vector space, including computation of the transition matrix
and
determining an orthonormal basis for the space.
18. Compute all the eigenvalues of a square matrix, including any complex eigenvalues, and
determine
their corresponding eigenvectors.
19. Determine if a square matrix is diagonalizable and compute the diagonalization of a matrix
whose
eigenvalues are easily calculated.
20. Perform linear transformations among abstract general vector spaces, determining the rank,
the nullity
and the associated matrix of the transformation.
College policy on attendance:
1. Attendance shall be taken and recorded at each regularly scheduled class
Meeting.
2. Any student accumulating absences, which exceed 6% of the total hours,
may be dropped and if absences exceed 12% he or she must be dropped.
3. Two days of tardiness or leaving early may be treated as one absence.
4. Whenever the professor is absent from class because of emergency or
illness and a substitute is not assigned, students may leave after 15 minutes.
Course Content:
1. Systems of Linear equations (ch. 1)
2. Matrices & Determinants. (ch. 2 & 3)
3. Vector Spaces & Inner Product Spaces (ch. 4 & 5)
4. Linear Transformations (ch. 6)
5. Eigenvalues and Eigenvectors (ch. 7)
Methods of Evaluation:
1. Homework: Problems will be assigned every class day and will be
collected every Monday. No late home work. You should hand in at least
ten homework assignments (a one week assignment counted as one home
work) to get full credit.
2. Quiz: There will be one take-home quiz. The Quiz will be distributed on
Tuesday as scheduled in the attached sheet and will be collected on
Thursday. No make-up or late quiz.
3. Test: There will be three in class tests. All tests are important. No make
up tests except on medical reasons with doctor’s note and on
emergency’s with valid documentation.
4. Final Exam: There will be a final exam on the last day of class.
Calculators: You may use any scientific calculator but no graphing
calculators.
Grading: The final grade points will be determined as follows:
Homework 100
Quiz
100
Test
600
Final
200
Extra credit 50
The planned grading standard for the class is
A = 90 – 100 %
B = 80 – 89 %
C = 70 – 79 %
D = 60 – 69 %
F = below 60 %.
Behavior Policy: Please read Policy 3100. If you exhibit deliberate behavior
which prohibits or impedes any member of the class from pursuing any class
assignment, objective or learning opportunity within the classroom, you will
be asked to leave the class and appropriate action will be taken, in
accordance with policy 3100.
Cheating Policy: Any student caught cheating will receive a “0” grade on
that assignment, may fail in the course and/or will be reported to the Student
Affairs Office for disciplinary action.
Note: Students with disabilities who may need academic accommodations
should discuss options with their professors during the first week of class.
Mathematics 254 – Tentative Schedule
Spring 2016 (1/25/2016 – 5/21/2016)
Monday
1/25
1.1
2/1
2.1,2.2
2/8
2.3,2.4
2/15
Washington’s Day
2/22
3.1,3.2
2/29
4.1,4.2
3/7
4.3,4.4
3/14
4.5,4.6(take home
quiz)
3/21
4.7,4.8
3/28
Recess
4/4
5.1,5.2
4/11
5.4,5.5
4/18
6.1,6.2
4/25
Test#3
5/2
6.5
5/9
7.2,7.3
5/16
Review
Tuesday
1/26
2/2
2/9
2/16
2/23
3/1
3/8
3/15
3/22
3/29
Recess
4/5
4/12
4/19
4/26
5/3
5/10
5/17
Wednesday
1/27
1.2,1.3
2/3
2.2,2.3
2/10
2.4,2.5
2/17
Test#1
2/24
3.3,3.4
3/2
4.2,4.3
3/9
4.4,4.5
3/16
4.7
Thursday
Friday
1/29
1/29
2/4
2/5
2/11
2/18
2/12
Lincoln’s Day
2/19
2/25
2/26
3/3
3/4
3/10
3/11
3/17
3/18
3/23
Test#2
3/30
Recess
4/6
5.3,5.4
3/24
3/25
4/7
4/8
4/13
5.5
4/20
6.2,6.3
4/27
6.4,6.5
5/4
7.1,7.2
5/11
7.3,7.4
5/18
Final Exam
4/14
Withdrawal
deadline
4/15
4/21
4/22
4/28
4/29
5/5
5/6
5/12
5/13
5/19
5/20
3/31
4/1
Recess
Recess