# SRJC Course Outlines

 5/25/2024 12:44:44 AM MATH 5 Course Outline as of Fall 1999 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
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.

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.