# Math 317 – Theory of Linear Algebra

## Course Coordinator

Scott Hansen

shansen@iastate.edu

## 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.

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