| 4/20/2024 7:54:34 AM |
| Changed Course |
| CATALOG INFORMATION
|
| Discipline and Nbr:
MATH 5 | Title:
LINEAR ALGEBRA |
|
| Full Title:
Linear Algebra |
| Last Reviewed:2/8/2021 |
| Units | Course Hours per Week | | Nbr of Weeks | Course Hours Total |
| Maximum | 3.00 | Lecture Scheduled | 3.00 | 17.5 max. | Lecture Scheduled | 52.50 |
| Minimum | 3.00 | Lab Scheduled | 0 | 17.5 min. | Lab Scheduled | 0 |
| | Contact DHR | 0 | | Contact DHR | 0 |
| | Contact Total | 3.00 | | Contact Total | 52.50 |
| |
| | Non-contact DHR | 0 | | Non-contact DHR Total | 0 |
| | Total Out of Class Hours: 105.00 | Total 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:
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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: | Transferable | Effective: | Spring 1989 | Inactive: | |
| |
| UC Transfer: | Transferable | Effective: | Spring 1989 | Inactive: | |
| |
| 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:
At the conclusion of this course, the student should 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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