Math 317 – Theory of Linear Algebra

Course coordinator

Scott Hansen
shansen@iastate.edu
515-294-8171

Catalog description

MATH 317: Theory of Linear Algebra

(4-0) Cr. 4. F.S.

Prereq: Credit or enrollment in MATH 201
Systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Emphasis on writing proofs and results. Only one of MATH 207 and MATH 317 may be counted toward graduation.

Textbook

Elementary Linear Algebra, 5th Edition
Andrilli and Hecker
ISBN: 9780128008539

Syllabus

Suggested lecture timetable includes 3 test days (included with each of Chapters 3, 4 and 5), each with a review day. Two review days are left over for the final exam review. Chapters 1-6 are organized in a sequential fashion, and the timetable below is based on coverage of the sections in sequential order. However the instructor is encouraged to introduce central concepts from Chapters 4-6 ahead of time, and adjust the timetable accordingly. Chapter 7 and applications topics from Chapters 8,9 can optionally be covered as time permits.

Chapter 1 – Vectors and Matrices (6 lectures)
- Sections 1.1-1.5, 1.3(optional/lightly review)
Chapter 2 – Systems of Linear Equations (7 lectures)
- Sections 2.1-2., 2.3(cover lightly)
Chapter 3 – Determinants and Eigenvalues (8 lectures)
- Sections 3.1-3.4, Test 1, Section 3.3 (lightly)
Chapter 4 – Finite Dim’l Vector Spaces (15 lectures)
- Sections 4.1-4.7, Test 2, Section 4.6 (limit to 1 lecture)
Chapter 5 – Linear Transformations (14 lectures)
- Section 5.1-5.6, Test 3
Chapter 6 – Orthogonality (7 lectures)
- Sections 6.1-6.3, optional applications in Sections 8,9

Objectives for Math 317

Be able to:

use vector algebra, matrix algebra and dot products to manipulate vector and matrix equations.
find the solution set to a given linear system of equations in parametric form.
compute the echelon and reduced echelon forms of a matrix .
compute row space, column space, null space, left null space, rank of a matrix.compute inverse matrices.
compute orthogonal projections on to vectors and hyperplanes.
compute determinants, and understand the basic properties of determinants.
compute orthogonal complements of a subspace
determine the dimension of a vector subspace
compute the standard matrix for a given linear transformation.
compute the matrix for a linear transformation with respect to a given basis.
compute an orthogonal basis from one that is not orthogonal.
find an orthogonal matrix that diagonalizes a given symmetric matrix.

Be able to prove simple theorems on fundamental properties of linear algebra. These could include the following.

Prove a given set is a subspace (or prove it is not).
Prove a given set of vectors is linearly independent (or prove it is not).
Prove a given transformation is linear (or is not).
Use key theorems such as the Dimension Theorem to deduce properties of a given linear transformation.
Prove whether a set of vectors forms a basis.

Free expression statement

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Students with disabilities

Iowa State University is committed to assuring that all educational activities are free from discrimination and harassment based on disability status. Students requesting accommodations for a documented disability are required to work directly with staff in Student Accessibility Services (SAS) to establish eligibility and learn about related processes before accommodations will be identified. After eligibility is established, SAS staff will create and issue a Notification Letter for each course listing approved reasonable accommodations. This document will be made available to the student and instructor either electronically or in hard-copy every semester. Students and instructors are encouraged to review contents of the Notification Letters as early in the semester as possible to identify a specific, timely plan to deliver/receive the indicated accommodations. Reasonable accommodations are not retroactive in nature and are not intended to be an unfair advantage. Additional information or assistance is available online at www.sas.dso.iastate.edu, by contacting SAS staff by email at accessibility@iastate.edu, or by calling 515-294-7220. Student Accessibility Services is a unit in the Dean of Students Office located at 1076 Student Services Building.

More information about disability resources in the Mathematics Department can be found at https://iastate.app.box.com/s/c17d3ljul83lujr2j1mdeqoqcdqiva1t.