M TH 543 - A BSTRACT L INEAR A LGEBRA
O REGON S TATE U NIVERSITY
FALL 2011
T EXT: NONE
L ECTURE N OTES
Vector Spaces
Denition: Let F be a set with at least two elements, and with two binary operations, +, .
Then F is a eld under these operations if
(1) F
Chapter 1 Vectors
Section 1.1 The Geometry and Algebra of Vectors
Pg 3,
Pg 10, Theorem 1.1 Algebraic Properties of Vectors in Rn Let u, v, and w be vectors in Rn and let c and d be
scalars. Then
a.
(Commutativity)
b.
(Associativity)
c.
d.
e.
(Distributivi
Chapter 2 Systems of Linear Equations
Section 2.1 Introduction to Systems of Linear Equations
Pg 59, Definition A linear equation in the n variables is an equation that can be written in the form
where the coefficients and the constant term b are constant
Chapter 3 Matrices
Section 3.1 Matrix Operations
Pg 136, Definition A matrix is a rectangular array of numbers called the entries, or elements of the matrix.
Pg 139, Definition If A is an matrix and B is an matrix, then the product C = AB is an matrix. Th
Chapter 4 Eigenvalues and Eigenvectors
Section 4.1 Introduction to Eigenvalues and Eigenvectors
Pg 253, Definition Let A be an matrix. A scalar is called an eigenvalue of A if there is a nonzero vector x such
that . Such a vector x is called an eigenvecto
Abstract Linear Algebra Notes
9/26
Definition Let F be a set with at least two elements. Then is a field if:
1. F is an abelian group under + with additive identity element 0;
2. F\cfw_0 is an abelian group under with multiplicative identity 1;
3. Distrib
Conjecture: If p is prime, then p is a factor of (p-1)!+1.
Or MAYBE:
Conjecture: p is prime iff p is a factor of (p-1)!+1. This second conjecture may be a long
stretch!
Pg 206, #48
A cigar manufacturer produces x cases of cigars per day at a daily cost of
dollars. Show that his cost increases and his average cost decreases as the output x increases.
Pg 206, #48
A cigar manufacturer produces x cases of cigars per day at a
To create a blank grid change your x and y min and max. Either use Excel to set final min and max, or adjust yours.
x
y
-10
0
10
-10
0
10
min
15
max
10
5
0
-15
-10
-5
0
-5
-10
-15
5
10
15
Name _
Date _
MTH 65 T. Lingo
Chapter 9 Quiz
Follow the directions for each problem. Good luck!
Solve. Express the solution in interval notation.
1.
2. 5(x + 4) 17 > 3 + 10(3 + x)
Write a linear inequality and solve.
3. You decide to start a business sell
Problem 5
The class mean of the number in a family is 4.5.
Here are eight distributions with the mean of 4.5 and sample size of 16.
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Mean
MAD
2
3
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
4.5
0.5
6
5
3
4
5
2
5
5
5
6
5
6
4
5
2
The knees are one of the highest impact areas of the body and it is therefore vital to undertaken
knee strengthening exercises to help protect the muscles from wear and tear. As with any form of
strengthening exercises though it is important to remember t
Chest and Back
Shoulders and Arms
Standard Push-Ups
Alternating Shoulder Press
Wide Front Pull-Ups
In & Out Bicep Curls
Military Push-Ups
Two-Arm Triceps Kickbacks
Reverse Grip Chin-Ups
Deep Swimmer's Press
Wide Fly Push-Ups
Full Supination Concentration
There is $320 available to fence in a rectangular garden. The fencing for the side of the
garden facing the road costs $6 per foot and the fencing for the other three sides costs $2 per
foot. Find the dimensions of the largest possible garden.
a)
b)
Expr