Math 317 - Theory of Linear Algebra - Sections 2 and 3

Instructor: Jonas Hartwig jth@iastate.edu Office: Carver 470, office hours TF 3-4.
TA/Grader: Issac Odegard. Office 477, office hour W 2-3.

Course Log and Homework Assignments

Click here for a list of recommended practice problems.

Aug 26-30: §1.1, §4.1, §1.2.  HW: §1.1 #11,20,22a
Sep 2-6: §1.4, §1.5, §2.1.   HW: §1.2: #8,10; §1.4: #6,13b
Sep 9-13: §2.2, §2.3, §2.4.   HW: §1.5: #28ab; §2.1: #5
Sep 16-20: §2.4, §3.1, §3.2.   HW: §2.2: #9,11a; §2.3: #8b; §2.4: #7b,14bc
Sep 23-27: §3.4 Thursday Exam 1 on Ch.1 & Ch.2   HW: §3.1: #5b,9b,11b; §3.2: #2d,5,7
Sep 30-Oct 4: §3.4, §4.1.   HW: §3.4: #1bd, 2b, 6, 13
Oct 7-11: §4.1, §4.2.   HW: §3.4: #4g,5a; §4.1: #8,11,13a
Oct 14-18: §4.3, §4.4, §4.5.   HW: §4.2: #2fg,3cdh,19
Oct 21-25: §4.5, §4.6, §4.7.   HW: §4.3: #8,9; §4.4: #2a,4f,5,14
Oct 28-Nov 1: Review. Thursday Exam 2 on Ch.3 & Ch. 4 (excluding transition matrices).   HW: §4.5: #1c,7; §4.6: #1b,5b,10b,11b; §4.7: #1fi
Nov 4-8: §5.1, §5.2.   HW: §5.1: #16,17,23
Nov 11-15: §5.3, §5.4.   HW: §5.2: #7b, 12ab,16abc;
Nov 18-22: §5.5. Thursday Exam 3 on Ch.5(§5.1-§5.5)   HW: §5.3: #1bd,9; §5.4: #2b,4ab,5ab
Nov 25-29: Thanksgiving break
Dec 2-6: §5.6, §6.1   HW (due Monday Dec 9): §5.6: #1b, 2a, 10
Dec 9-13: Euclidean spaces; Review.   HW §6.1: #2d,4bd,9ab;
Dec 16-20: Finals week

Final Exam
MATH 317 Section 2: Thursday December 19 at 12:00 PM
MATH 317 Section 3: Tuesday December 17 at 2:15 PM

Catalog Description

MATH 317. Theory of Linear Algebra.
(4-0) Cr. 4. F.S.SS. 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

book coverAndrilli and Hecker
Elementary Linear Algebra
5th Edition
ISBN: 978-0-12-800853-9


Syllabus

Chapter 1: Vectors and Matrices (6 lectures)
Chapter 2: Systems of Linear Equations (7 lectures)
Chapter 3: Determinants and Eigenvalues (8 lectures)
Chapter 4: Finite-Dimensional Vector Spaces (16 lectures)
Chapter 5: Linear Transformations (15 lectures)
Chapter 6: Orthogonality (7 lectures)

Grading

Homework: 20%
In-class activities: 15%
Exams 1-3: 15% each
Final: 20%

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.

Old Exams

Sample Final With Solutions

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