# SRJC Course Outlines

 4/1/2023 11:25:05 PM MATH 5 Course Outline as of Spring 2010 Changed Course CATALOG INFORMATION Discipline and Nbr:  MATH 5 Title:  INTRO TO LINEAR ALGEBRA Full Title:  Introduction to 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
Repeatability:  00 - Two Repeats if Grade was D, F, NC, or NP
Also Listed As:
Formerly:

Catalog Description:
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An introduction to linear algebra including the theory of matrices, determinants, vector spaces, linear transformations, eigenvectors, eigenvalues and applications.

Prerequisites/Corequisites:
Completion of MATH 1B or higher (VF)

Recommended Preparation:
Concurrent enrollment in MATH 1C or MATH 2

Limits on Enrollment:

Schedule of Classes Information
Description: Untitled document
An introduction to linear algebra including the theory of matrices, determinants, vector spaces, linear transformations, eigenvectors, eigenvalues and applications.

Prerequisites:Completion of MATH 1B or higher (VF)
Recommended:Concurrent enrollment in MATH 1C or MATH 2
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: Major Applicable Course

COURSE CONTENT

Outcomes and Objectives:
At the conclusion of this course, the student should be able to:
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Upon successful completion of the course, students will be able to:
1. Solve systems of linear equations using Gauss-Jordan elimination and Cramer's rule.
2. Define operations on matrices, invertibility, elementary matrices, orthogonal matrices.
3. Apply properties of determinants to matrices.
4. Evaluate determinants using row reduction techniques.
5. Define cofactors and adjoints of determinants to determine the inverse of a matrix.
6. Define properties of vectors, subspace, span, linear independence,
bases, inner product spaces, and orthonormal bases.
7. Define and determine dimension rank of solution space of a system of linear equations.
8. Define kernel, range, rank, nullity, matrix representation of
linear transformation, similarity, and change of basis.

Topics and Scope
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I.   Matrices
A.  Systems of linear equations
B.  Gauss-Jordan elimination
C.  Operations on matrices
D.  Invertibility
E.  Elementary matrices
F.  Orthogonal matrices
II.  Determinants
A.  Properties
B.  Evaluation by row reduction
D.  Formula for inverse of a matrix
E.  Cramer's rule
III. Vector Spaces
A.  Defining properties
B.  Subspace
C.  Span
D.  Linear independence
E.  Basis
F.  Dimension
G.  Rank
H.  Solution space of a system of linear equations
I.  Inner product spaces
J.  Orthonormal bases
K.  Gram-Schmidt process
IV.  Linear Transformations
A.  Kernel
B.  Range
C.  Rank and nullity
D.  Matrix representation of linear transformation
E.  Similarity
F.  Change of basis
V.   Eigenvectors and Eigenvalues
A.  Characteristic equations
B.  Eigenspaces
1.  Diagonalization of matrices
2.  Orthogonal diagonalization of symmetric matrices
VI.  Applications may include:
A.  Differential equations
B.  Fourier series
D.  Gauss-Seidel method
E.  Partial pivoting
F.  Eigenvalue approximation
G.  Others

Assignments:
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1.  Reading outside of class (0-50 pages per week)
2.  Problem set assignments (15-30)
3.  Midterm exams (2-5), quizzes (0-20) and final exam