SRJC Course Outlines

9/24/2022 8:49:25 AMMATH 5 Course Outline as of Fall 1999

Changed Course
CATALOG INFORMATION

Discipline and Nbr:  MATH 5Title:  LINEAR ALGEBRA  
Full Title:  Linear Algebra
Last Reviewed:2/8/2021

UnitsCourse Hours per Week Nbr of WeeksCourse Hours Total
Maximum3.00Lecture Scheduled3.0017.5 max.Lecture Scheduled52.50
Minimum3.00Lab Scheduled017.5 min.Lab Scheduled0
 Contact DHR0 Contact DHR0
 Contact Total3.00 Contact Total52.50
 
 Non-contact DHR0 Non-contact DHR Total0

 Total Out of Class Hours:  105.00Total Student Learning Hours: 157.50 

Title 5 Category:  AA Degree Applicable
Grading:  Grade Only
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As: 
Formerly: 

Catalog Description:
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A complete lower division course in Linear Algebra including the theory of matrices, determinants, vector spaces, linear transformations, eigenvectors, eigenvalues and applications.

Prerequisites/Corequisites:
Math 1B.


Recommended Preparation:
Concurrent enrollment in Math 2A or 2B.

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
Matrices, determinants, vector spaces, linear transformations, eigenvectors & eigenvalues, applications.
(Grade Only)

Prerequisites:Math 1B.
Recommended:Concurrent enrollment in Math 2A or 2B.
Limits on Enrollment:
Transfer Credit:CSU;UC.
Repeatability:00 - Two Repeats if Grade was D, F, NC, or NP

ARTICULATION, MAJOR, and CERTIFICATION INFORMATION

Associate Degree:Effective:Inactive:
 Area:
 
CSU GE:Transfer Area Effective:Inactive:
 
IGETC:Transfer Area Effective:Inactive:
 
CSU Transfer:TransferableEffective:Spring 1989Inactive:
 
UC Transfer:TransferableEffective:Spring 1989Inactive:
 
C-ID:
 CID Descriptor: MATH 250 Introduction to Linear Algebra SRJC Equivalent Course(s): MATH5

Certificate/Major Applicable: Not Certificate/Major Applicable



COURSE CONTENT

Outcomes and Objectives:
Upon completion of the course, students will be able to:
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01 Solve systems of linear equations with Gauss-Jordan elimination.
2. Define operations on matrices, inveribility, elementary matrices,
  orthogonal matrices.
3. Apply properties of determinants, evaluation by row reduction.
4. Define cofactors and adjoint, formula for inverse of a matrix, Cramer's
  rule.
5. Define properties of vectors, subspace, span, linear independence,
  basis, dimension, rank, solution space of a system of linear equations,
inner product spaces, orthonormal bases.
6. Define kernel, range, rank/nullity theorem, matrix representation of
  linear transformation, similarity, change of basis.

Topics and Scope
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1.  Matrices.
    Systems of linear equations, Guass-Jordan elimination, operations
    on matrices, invertibility, elementary matrices, orthogonal
    matrices.
2.  Determinants.
    Properties, evaluation by row reduction, cofactors and adjoint,
    formula for inverse of a matrix, Cramer's rule.
3.  Vector Spaces.
    Defining properties, subspace, span, linear independence, basis,
    dimension, rank, solution space of a system of linear equations,
    inner product spaces, orthonormal bases, Gram-Schmidt process.
4.  Linear Transformations.
    Kernel, range, rank/nullity theorem, matrix representation of
    linear transformation, similarity, change of basis.
5.  Eigenvectors and Eigenvalues.
    Characteristic equations, eigenspaces (diagonalization of matrices,
    orthogonal diagonalization of symmetric matrices).
6.  Applications (time permitting).
    Differential equations, Fourier series, quadratic forms,
    Gauss-Seidel method, partial pivoting, eigenvalue approximation,
    others.

Assignments:
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1.  The student will have daily outside reading, problem set assignments
   from required text(s), or instructor chosen supplementary materials.
2.  Instructional methodology may include, but not limited to: lecture,
   demonstrations, oral recitation, discussion, supervised practice,
   independent study, outside project or other assignments.

Methods of Evaluation/Basis of Grade.
Writing: Assessment tools that demonstrate writing skill and/or require students to select, organize and explain ideas in writing.Writing
0 - 0%
None
This is a degree applicable course but assessment tools based on writing are not included because problem solving assessments and skill demonstrations are more appropriate for this course.
Problem solving: Assessment tools, other than exams, that demonstrate competence in computational or non-computational problem solving skills.Problem Solving
25 - 50%
Homework problems, Exams
Skill Demonstrations: All skill-based and physical demonstrations used for assessment purposes including skill performance exams.Skill Demonstrations
30 - 70%
Performance exams
Exams: All forms of formal testing, other than skill performance exams.Exams
5 - 25%
Multiple choice
Other: Includes any assessment tools that do not logically fit into the above categories.Other Category
0 - 0%
None


Representative Textbooks and Materials:
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Text(s) required of each student will be selected by the department,
a committe of the department, or the responsible instructor from the
books currently available. Choices in the past have included:
 ELEMENTARY LINEAR ALGEBRA (7th) Howard Anton, Wiley, 1997.
 ELEMENTARY LINEAR ALGEBRA (3rd) Heath 1996.

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