## MATH369 Linear Algebra, Spring 2009, Section 2, Noon

### Objectives

Introduction to Linear Algebra: linear equations, matrices, determinants, Euclidean space, dot product, abstract vector spaces, basis and linear independence, linear maps, eigenvalues, eigenvectors, base change, orthogonality, Gram-Schmidt, applications.
### General Information

Instructor: Anton Betten, room 207, Weber building.

Email lastname at math dot colostate dot edu

Course website: http://www.math.colostate.edu/ betten/courses/MATH369/SP09/369_syllabus.html http://www.math.colostate.edu/ betten/courses/MATH369/SP09/369_syllabus.html

Credits: 3

Class: M W F Noon - 1pm, ENGRG E 104

Prerequisites: MATH161

Text: Steven J. Leon, Linear Algebra with Applications, ISBN 0-13-185785-1

Homework: 10 assignments. Due Wednesdays. Precise due dates:
HW1 is due 1/28,
HW2 is due 2/4,
HW3 is due 2/11,
HW4 is due 2/25,
HW5 is due 3/4,
HW6 is due 3/11,
HW7 is due 4/1,
HW8 is due 4/8,
HW9 is due 4/15,
HW10 is due 4/29.
no late homework is accepted
Quizzes: the even weeks unless there is a midterm (1/30, 2/27, 4/3, 5/1)
Office hours: Monday, Wednesday 10:30-11:30.
Extra office hours by Dr. Painter: Monday 2-4, Tuesday 10-12.

### Exams

Midterms (Wednesdays):

Midterm 1: week 4, i.e. 2/11

Midterm 2: week 8, i.e. 3/11

Midterm 3: week 12, i.e. 4/15

Final: Monday 7am during finals week in the classroom. Calculators OK.
### Grading

HW+QUIZZES = 100, each Midterm = 100, Final = 200. Total 600.

greater or equal 540 = A,

greater or equal 480 = B,

greater or equal 420 = C,

greater or equal 360 = D.

We grade one hw problem each week (at random), worth 10 points. The HW grades count to a maximum of 60. Each Quiz is worth 15 points. The Quizzes count to a maximum of 40.
### Syllabus

Weeks 1-4: Linear systems, homogeneous/inhomogeneous systems, REF and RREF, matrix algebra, complex numbers as 2 by 2 matrices, matrix product, transposed matrix, dot poduct, inverse matrix, determinants of 2 by 2 matrices, regular vs. singular matrices, elementary matrices, inverse matrix, LU decomposition, abstract vector spaces, polynomials.

Weeks 5-8: Determinants, more on vector spaces, infinite dimensional spaces, vector space of sequences, function spaces, Euclidean space, length and angle, span, sum, subspace, linear dependence and independence, bases, dimension, matrices and linear maps, range, kernel, isometries in Euclidean space, rotation and reflection.

Weeks 9-12: invariant subspaces, characteristic polynomial, eigenvalues, eigenvectors, base change.

Weeks 13-15: inner product spaces, orthogonality, orthonormal bases, orthogonal projection, Gram-Schmidt, QR decomposition, least squares, permutations, even and odd, determinants (Laplace).

### Homework:

See here

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On 11 May 2009, 15:28.