LINEAR ECONOMIC MODELS
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
I NTRODUCTION
When society has grown mo
Lecture Note 15
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
L ENGTH IN R2 AND R3
ENGTH IN
R2 AND R3
2
Let
Lecture Note 16
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
O R THONORMAL B ASES IN Rn
RTHONORMAL
B ASES I
Lecture Note 17
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
O R THOGONAL C OMPLEMENTS
RTHOGONAL
C OMPLEMEN
Lecture Note 19
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
E IGNEVALUES , E IGENVECTORS , AND D IAGONALIZATION
1. Eignevalues
Lecture Note 20
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
E IGNEVALUES , E IGENVECTORS , AND D IAGONALIZATION
1. Eignevalues
Partitioned Matrix
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
M ATRIX O PERATIONS : PAR TITIONING
ATRIX
O
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 1
Due Date: 29th January, 2010 (Friday)
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 2
Due Date: February 24, 2010
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regul
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 3
Due Date: 12th March, 2010
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regula
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 4
Due Date: 31th March, 2010
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regula
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 5
Due Date: 19th April 2010
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulat
Lecture Note 13
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
R EAL V ECTOR S PACES
1. Coordinates and Change of Basis
EAL
V ECTO
Lecture Note 12
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
Matrix Transformations
Linear Transformations
Produced by Jeff Ch
Lecture Note 3-1
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
S OLUTIONS OF L INEAR S YSTEMS OF E QUATIONS
OLUTIONS OF
L INEAR S
Lecture Note 1
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
Lecture Notes
Go to
http:/www.math.cuhk.edu.hk/
Lecture Note 2
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
L INEAR E QUATIONS AND M ATRICES
1. Linear Syst
Lecture Note 3
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
L INEAR E QUATIONS AND M ATRICES
1. Linear Syst
Lecture Note 4
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
S OLVING THE L INEAR S YSTEMS
Gaussian Elimination and LU Factorizat
Lecture Note 5
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
E LEMENTARY M ATRICES
LEMENTARY
M ATRICES
2
We have seen that any ma
Lecture Note 6
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
D ETERMINANTS
1. Denition and Properties
2. Cofactor Expansion and A
Lecture Note 7
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2009
Produced by Jeff Chak-Fu WONG
1
R EAL V ECTOR S PACES
1. Vector Spaces
2. Subspaces
3. Linear Indepe
Lecture Note 9
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
R EAL V ECTOR S PACES
1. Vector Spaces
2. Subspaces
3. Linear Indepe
Lecture Note 10
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
jwong@math.cuhk.edu.hk
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
R EAL V ECTOR S PACES
1. Vector Spaces
2. Subs
Lecture Note 11
Dr. Jeff Chak-Fu WONG
Department of Mathematics
Chinese University of Hong Kong
MAT 2310
Linear Algebra and Its Applications
Winter, 2010
Produced by Jeff Chak-Fu WONG
1
R EAL V ECTOR S PACES
1. Vector Spaces
2. Subspaces
3. Linear Indep
THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MAT2310 Linear Algebra and Applications (Winter 2010)
Homework 6
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on honesty in academi