# SRJC Course Outlines

 6/10/2023 2:07:47 PM MATH 5 Course Outline as of Fall 2021 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 4.00 Lecture Scheduled 4.00 17.5 max. Lecture Scheduled 70.00 Minimum 4.00 Lab Scheduled 0 17.5 min. Lab Scheduled 0 Contact DHR 0 Contact DHR 0 Contact Total 4.00 Contact Total 70.00 Non-contact DHR 0 Non-contact DHR Total 0

 Total Out of Class Hours:  140.00 Total Student Learning Hours: 210.00

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 (MATH)

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 (MATH)
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

Student Learning Outcomes:
At the conclusion of this course, the student should be able to:
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1.  Determine the dimensions of a variety of vector spaces.
2.  Find eigenvalues, eigenvectors and eigenspaces of matrices and linear transformations.
3.  Determine matrix representations of linear transformations and linear operators.

Objectives: Untitled document
Students will be able to:
1.   Solve systems of linear equations using Gauss-Jordan elimination, matrix inverses and
Cramer's rule.
2.   Define matrix operations, invertibility, elementary matrices and orthogonal matrices.
3.   Use properties of determinants including row reduction to evaluate determinants.
4.   Invert matrices using adjoints and cofactors.
5.   Define vector spaces, subspaces, span, linear independence, bases, dimension, inner product
spaces, and orthonormal bases.
6.   Determine the nullspace or kernel and range of a matrix and linear transformation.
7.   Determine the injectivity and surjectivity of linear transformations and linear operators.
8.   Define and determine dimension, rank and nullity of a matrix.
9.   Determine the matrix representation of a linear transformation using different bases and
using change of basis.
10. Determine eigenvalues, eigenvectors and eigenspaces of matrices and linear transformations.
11. Apply proof writing techniques to prove basic results in linear algebra.
12. Utilize methods of linear algebra to solve application problems selected from science,
engineering, and related fields.

Topics and Scope
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I. Vectors
A. Review of vectors in 2- and 3-dimensional real space
B. Vectors in n-dimensional real space
C. Properties of vectors in n-dimensional real space, including dot product, norm of a vector,
angle between vectors, and vector orthogonality
II. Matrices
A. Systems of linear equations
B. Gauss-Jordan elimination
C. Operations on matrices, including the transpose
D. Invertibility
E. Triangular matrices
F. Elementary matrices
G. Orthogonal matrices
III. Determinants
A. Properties
B. Evaluation by row reduction
D. Formula for inverse of a matrix
E. Cramer's rule
IV. Real 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
V. Linear Transformations
A. Kernel
B. Range
C. Rank and nullity
D. Matrix representation of linear transformation
E. Similarity
F. Change of basis
G. One-to-one and onto
VI. Eigenvectors and Eigenvalues
A. Characteristic equations
B. Eigenspaces
1. Diagonalization of matrices
2. Orthogonal diagonalization of symmetric matrices
VII. Proofs applied to:
A. Linear independence of vectors
B. Properties of subspaces
C. Linearity, injectivity and surjectivity of transformations
D. Properties of eigenvectors and eigenvalues
E. Vector spaces and subspaces
VIII. Applications including at least two of the following:
A. Differential equations
B. Fourier series
D. Gauss-Seidel method
E. Partial pivoting
F. Eigenvalues, eigenvalue approximations and eigenvectors
G. Markov chains
H. Computer graphics
I.  Graph theory networks
J. Dynamical systems
K. Cryptography
L. Least squares techniques
M. Recurrence relations
N. Balancing chemical equations
O. Leontief input-output model
P. QR decomposition
Q. Rotated conic sections
IX. Technology - Computer Algebra Systems

Assignments:
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1. Reading outside of class (5-50 pages per week)
2. Problem sets (15-30)
3. Midterm exams (2-5), quiz(zes) (0-20) and final exam
4. Project(s) (0-5), such as: computer labs, term projects, group projects