THE UNIVERSITY OF HON G KONG
DEPARTMENT OF MATHEMATICS
MATH1853 LINEAR ALGEBRA, PROBABILITY AND STATISTICS
December 12, 2013 (2:30pm 5:30pm)
Only approved calculators as announced by the Emamtnattons Secretary can be used
in this eaarninatton. It is oandt

THE UNIVERSITY OF HONG KONG
DECEMBER 2012 EXAMINATION
MATHEMATICS: PAPER MATH1853
LINEAR ALGEBRA, PROBABILITY AND STATISTICS
(To be taken by BEng & BEng(EngSc)students)
18 December, 2012 9:30am. w 12:30pm.
Only approved calculators as announced by the Exa

THE UNIVERSITY OF HONG KONG
MAY 2013 EXAMINATION
MATHEMATICS: PAPER MATH1853
LINEAR ALGEBRA, PROBABILITY AND STATISTICS
(To be taken by BEng, BEng(E1ecE), BEng(ME) & BEng(EngSc)students)
14 May, 2013 2:30pm. 7 5:30pm.
Only approved calculators as announce

1 1 1
S 0 , 1, 1
1 1 2
Does the set S SPAN R3 ?
1 1 1
S 0 , 1, 1
1 1 2
Does the set S SPAN R3 ?
Is every vector in R3 a linear combination
of the vectors in S?
x
1
1
1
y c1 0 c2 1 c3 1
z
1
1
2
For every vector in R

Exam/1853/WKC/12-13
UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853 Linear Algebra, Probability and Statistics
Final Exam
Date: 18 Dec. 2012
Answer All SIX Questions.
Please Use Separate Answer Books for Questions in Parts I & II.
Part I
1. (a)

(Dr. N. Wong 21.9.2015) An augmented matrix question from one of you, which I think I may just solve it as a
demonstration of this type of question involving pivot & free columns.
I use brackets to denote pivots for ease of typing. The steps should be obv

Tutorial One
1 Solve
1.
S l the
th ffollowing
ll i equations
ti
using
i Gaussian
G
i elimination.
li i ti
4x
y
t 4
x 4y z
y 4z
x
t
1
4
z 4t
10
Solution:
Write down the single matrix equation for the given equations, use
Gaussian elimination to make th

THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: LINEAR ALGEGRA, PROBABILITY AND STATISTICS
2:30p.m. - 5:30p.m.
May 13, 2014
Only approved calculators as announced by the Examinations Secretary can be used
in this examination. It is candida

THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: Linear Algebra, Probability and Statistics
May 15, 2015
9:30a.m.-12:30p.m.
Only approved calrnlators as announced by the Examinations Secretary can be used
in this examination. It is candidat

13
Bernoulli Experiment and Its Related Distributions
An experiment is called a Bernoulli experiment if there are only two possible
outcome: success with probability p and failure with probability (1 p) where
0 < p < 1.
We say X is a Bernoulli random vari

THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: LINEAR ALGEBRA, PROBABILITY AND STATISTICS
December 9, 2014
2:30pm - 5:30pm
Only approved calculators as announced by the Examinations Secretary can be used
in this examination. It is candida

THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853 LINEAR ALGEBRA, PROBABILITY AND STATISTICS
December 10, 2015
(9:30am - 12:30pm)
No calculators are allowed in this examination.
Answer ALL SEVEN questions
Please Use Separate Answer Books for

9 Oct 2014
Hi Students,
I have googled and compiled below a list of linear algebra sample questions and answers. I find it hard to
select sample questions on the internet one after one because there are numerous. Therefore, Ill advise
you to pick those yo

THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1853: Linear Algebra, Probability and Statistics
May 15, 2015
9:30a.m.12:30p.m.
Only approved calculators as announced by the Examinations Secretary can be used
in this examination. It is candidate

Linear Algebra, Probability and Statistics
MATH 1853
Eigenvalues and Eigenvectors
Let A be a n n matrix:
a11 " a1n
A= #
# .
a
n1 " a nn
We are interested in some vectors xs which are in the same direction as Ax. i.e.
Ax x
or
Ax = x
for certain . The v

4
Permutations and Combinations
In this section, we introduce some notations for counting permutations and combinations.
The symbol n! represents the product of all integers from 1 to n. In other words,
it means that
n! = n (n 1) (n 2) (n 3) 2 1.
For simp

MATH 1853 Linear Algebra, Probability and Statistics
Instructor: Dr. Guangyue HAN. Oce: Room 423, Run Run Shaw Building. Web:
http:/hkumath.hku.hk/ghan. Email: ghan@hku.hk. Consultation Hours: Tuesdays, Thursdays
10:30AM-12:00PM.
Demonstrator: Dr. Fai Lun

THE UNIVERSITY OF HONG KONG
MAY 2014 EXAMINATION
MATHEMATICS: PAPER MATH1853
1. (10 points) a) Put the complex number 1
3i into its polar form.
b) Given any R, put the complex number (cos + i sin )3 (sin + i cos )4
into the form a + bi, where a, b R.
c)

Linear Algebra, Probability and Statistics
MATH 1853
Vector products
1.
Inner Product Spaces
1.1 Dot (scalar) product in R 3
G
G
G G
If a and b are two vectors, their dot product or scalar product, written a b , is
defined as,
G
G
G
G
if a 0, b 0
G G a b

The University of Hong Kong
Department of Statistics & Actuarial Science
STAT2601A Probability and Statistics I
2012-2013 First Semester
Core course for Quantitative Finance, Risk Management and Statistics Majors (4-year curriculum):
STAT2601A
Probability

MATH 1853 Linear Algebra, Probability and Statistics
Instructor: Dr. Wai-Ki CHING
(Room 414, Run Run Shaw Building, Email: wching@hku.hk).
Consultation Hours: WED 14:0017:00.
Time Table: (A) 08:30-09:20 MON,TUE, FRI (P2) and (B) 13:30-14:20 MON,TUE, THU (