MATH 221: Introduction to Linear Algebra - Outline, Fall 2015
MONDAY
August
WEDNESDAY
24
26
Vectors and the dot product.
Course
Overview
31
Projection
onto a line.
FRIDAY
September
2 equations in
2 unknowns.
7
2
14
16
2 × 2 inverse
Matrix addition, products
and the transpose.
21
28
Vector Space and
the Column Space CA
5
The Null space N (A)
12
A 3 × 4 example.
11
A 3×4
example.
Pathway Holiday
Road to Glory
2 × 2 determinant
[ A | I ] ∼ [ I | A−1 ]
4
Normals
Example(2.3)
9
Labor Day
Holiday
28
18
Test I = 60 points
23
n × n determinant
Adjoint formula
Cramer’s rule - Theorem(3.26)
30 October
Linear independence,independence
dimension and basis.
7
The rank of A and
Rank of A =
the row space of A
Rank of AT
14
Review
Test II = 60 points
19
21
Orthogonal subspaces and
the subspace theorem.
26
28
Least squares approximation.
Eigenvalues and
Projections.
eigenvectors.
November
2
4
Diagonalization of the matrix A.
Connection of eigenvalues
Eigenvalue multiplicities.
The equation P −1 AP = Λ
with the determinant.
A 3 × 3 example.
9
11
Simple eigenvalues and
Veteran’s Day
Test III = 60 points
independent eigenvectors.
Thank a Veteran
16
18


1 −2 2
Symmetry and
Orthogonal matrices
A =  −2 α β 
2
β α
orthogonal matrices.
23
25
The Bazillion
Thanksgiving Holiday
dollar vector.
Think of the William Bradford story.
30 December
2
Conics and Quadratic
Review
Review
forms.
25
2
9
16
23
Dimension
Theorem
FINALS WEEK: December 7 -11
Your Final Exam December 10, from 8:00-9:50 a.m.
30
6
13
20
27
4