MA 250 - Linear Algebra

Description
MA 250 - Linear Algebra is an introduction to Linear Algebra. It covers vectors in two and three dimensional space, systems of linear equations, matrix algebra, linear transformations, vectors in Rn, subspaces, dependence, bases, and eigenvectors. It includes some work with proofs and some applications.

Credit Hours: 4
Contact Hours: 4
Prerequisites/Other Requirements: MA 133 (C or higher)
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corequisite(s): None
Academic Program Prerequisite: None
Consent to Enroll in Course: No Department Consent Required
Dual Enrollment Allowed?: Yes
Course Fees: $19.00
Number of Times Course can be taken for credit: 1
Programs Where This Course is a Requirement:
Pre-Physics, A.A. (General Transfer)

General Education Requirement:
None
General Education Learner Outcomes (GELO):
NA
Course Learning Outcomes:
1. Solve systems of linear equations using matrices and row reduction techniques.

2. Calculate the determinants of matrices and use them in identifying invertible matrices and characteristic polynomials.

3. Use Gauss-Jordan elimination to find inverses of matrices.

4. Analyze and prove whether sets of vectors in Rn, together with their operations, meet the requirements for vector spaces and subspaces.

5. Identify important components of vectors spaces such as basis sets, spanning sets, and dimension.

6. Identify important qualities of matrices such as the rank and row, column, and null spaces.

7. Determine an orthonormal basis of a vector space and using the Gram-Schmidt process.

8. Find eigenvectors, and eigenvalues, and use them in applications.

9. Perform factorizations of matrices such as LU and QR decomposition and applying the Spectral Theorem.

10. Find the matrix of a linear transformation and compute its range and kernel.

11. Use visual representations such as graphs, charts, or graphics to enhance the meaning of the message that is being communicated.

12. Complete work accurately, with attention to detail.
Course Outline:
I. Systems of Linear Equations

A. Row Reduction and Echelon Forms

II. Matrix Algebra

A. Determinants

B. Inverse Matrix

C. Gauss-Jordan Elimination

III. Vector Spaces

A. Definition of a Vector Space

B. Subspaces and Spanning Sets

C. Basis and Dimension

D. Linear Independence

E. Row, Column, Null Space, and Rank

IV. Orthogonality

A. Projections

B. Subspaces

C. Orthonormal Spaces and the Gram-Schmidt process for Orthonormalization

D. QR Decomposition (Orthogonal/Upper Triangular Factorization)

V. Eigenvalues and Eigenvectors

A. Characteristic Polynomials

B. Diagonalization

C. Eigenspace

D. Symmetric Matrices and the Spectral Theorem

VI. Linear Transformations

A. As Matrices

B. Kernel and Range

C. Applications

Approved for Online and Hybrid Delivery?:
Yes
Instructional Strategies:
Collaborative learning: 25-75%

Lecture: 10-75%

Technology supplemented instruction: 10-25%

Facilitated discussion: 10-75%
Mandatory Course Components:
Some proofs incorporated into class and homework. Some use of technology.
Equivalent Courses:
None

Name of Industry Recognize Credentials: NA

Course-Specific Placement Test: None
Course Aligned with ARW/IRW Pairing: N/A

Mandatory Department Assessment Measures:
None

Course Type:
Program Requirement- Offering designed to meet the learning needs of students in a specific GRCC program.
Course Format:
Lecture - 1:1
Total Lecture Hours Per Week: 4
People Soft Course ID Number: 105002
Course CIP Code: 27.01
Maximum Course Enrollment: 25
School: School of STEM
Department: Mathematics
Discipline: MA
First Term Valid: Fall 2019 (8/1/2019)
1st Catalog Year: 2019-2020
Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement), Other (list below)
Faculty Credential Requirement Details:
Master’s Degree in Mathematics, or in a closely related field with at least 18 semester hours of graduate work in mathematics. A strong background in Linear Algebra is required.

Major Course Revisions: N/A
Last Revision Date Effective: 20230222T14:23:50
Course Review & Revision Year: 2027-2028