Long & Synthetic Division of
Polynomials
Synthetic Division is a
condensed version of long
division that can be used when
the divisor is of the form x c
(where c is a real number).
Note that synthetic division will not work
in cases where the divisor does
Introduction to Linear Algebra
MATH 2000
Course Pack
(required)
Fall 2009
Instructor: Prof. Chris Donnelly
Section C1601
T/Th 12:30-1:55pm, CN-246
MATH 2000
Chapter 1: Systems of Linear Equations
1.1 Introduction to Systems of Linear Equations
Definition:
MATH 2000
Basic Set Notation
Symbol Example Meaning
xA
x is an element in the set A
xB
x is NOT an element in the set B
BA
B is a subset of A (B could be equal to A)
AB
A is a proper subset of B (A is a subset of B, but not equal to B)
AB
the intersection
MATH 2000
Blank A
0
1
B
2
Additional Cryptography Examples
C D
3 4
E
5
F
6
G H
7 8
I J K L M N O P Q R S T U V W X Y Z
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
5 4
Ex 1) (a) Use the matrix A =
to encode the message LINEAR ALGEBRA.
1 2
LINE
MATH 2000
Chapter 7: Eigenvalues and Eigenvectors
7.1 Eigenvalues and Eigenvectors
Definition: Let A be an n n matrix. The scalar is called an eigenvalue of A if there is a
nonzero vector x such that Ax = x. The vector x is called an eigenvector of A
corr
MATH 2000
Elementary Linear Algebra
Section 1.1, Examples 4 & 5
and an Introduction to Matrices
Instructor: Prof. Donnelly
x1 +x2 +x3 =2 Already have leading coeff. of 1
x1 +3x2 +2 x3 =8 Add eqn. 1 to eqn. 2
4 x +x
=4 Add -4 eqn. 1 to eqn. 3
1 2
Mul