The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
(MATH2121)[2015](f)final~=5oh9b08kvq^_23515.pdf downloaded by whbchan from http:/petergao.net/ustpastpaper/down.php?course=MATH2121&id=4 at 20170205 00:11:53. Academic use within HKUST only.
4
2
1.
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
(MATH111)[2010](s)final~cs_zxxab^_10439.pdf downloaded by ccmakad from http:/petergao.net/ustpastpaper/down.php?course=MATH111&id=8 at 20161225 04:11:45. Academic use within HKUST only.
FINAL EXAM M
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 4
Last time: Vectors
A (column) vector
v=
v1
v2
.
.
vn
is matrix with one column. A vector has the same data as a list of real numbers.
The dimension of
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 12
Last time: introduction to determinants
Let n be a positive integer.
A permutation matrix is a square matrix whose entries are all 0 or 1, and which h
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 2
Last time: linear systems and row operations
Heres what we did last time: a system of linear equations or linear system is a list of equations
a11 x1 +
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 23
Last time: leastsquares problems
Definition. If A is an m n matrix and b Rm , then a leastsquares solution to the linear system
Ax = b is a vector x
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 21
Last time: orthogonal vectors and projections
The inner product or dot product of two vectors
u1
u2
u= .
.
.
un
and
v1
v2
.
.
vn
in Rn is the sca
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 3
Last time: row reduction to (reduced) echelon form
The leading entry in a nonzero row of a matrix is the first nonzero entry from left going right. For
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 10
Last time: inverses and subspaces
To show that an n n matrix A is invertible, all we have to do is check that (1) its columns are linearly
independent
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 9
Last time: inverses
The transpose of an m n matrix A is the n m matrix AT whose rows are the columns of A.
T
a d
a b c
For example,
= b e .
d e f
c f
I
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 19
Last time: complex eigenvalues
Write C for the set of complex numbers cfw_a + bi : a, b R.
Each complex number is a formal linear combination of two r
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 22
Last time: orthonormal vectors, projections, orthogonal bases
Vectors u1 , u2 , . . . , up are orthonormal if each ui is a unit vector and any two vec
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 11
Last time: theorems about bases and rank
A subspace of Rn is a nonempty subset H with the property that u + v H and cv H whenever
u, v H and c R. (Req
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 6
Last time: linear transformations
Notation. Writing
f :XY
means that f is a function which takes inputs from the set X and produces outputs in the set
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MIDTERM SOLUTIONS  MATH 2121, FALL 2017.
Name:
Email:
Problem # Max points possible Actual score
1
15
2
20
3
15
4
20
5
20
6
10
Total
100
You have 120 minutes to complete this exam.
No books, notes, o
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
M A T H 31 21
(MATH2121)[2011](f)midterm~=7femuej^_20373.pdf downloaded by ccmakad from http:/petergao.net/ustpastpaper/down.php?course=MATH2121&id=1 at 20160913 01:05:33. Academic use within HKUST
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
(MATH2121)[200X](f)quiz~=lqj1u^_20626.pdf downloaded by ccmakad from http:/petergao.net/ustpastpaper/down.php?course=MATH2121&id=0 at 20160913 01:05:36. Academic use within HKUST only.
MATH 2121 Lin
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Math 2121 Linear Algebra Spring 2017
1. Instructor
WeiPing LI
Email: [email protected] Room 3427
2. Teaching Assistant
Zhenzhen Li
Email: [email protected] Room 3212
3. Class Time and Venue
Lecture:
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Information about Final Exam of Math 2121
The final exam will covers the following sections: Chapter 1. Sections 1,
2, 3, 4, 5, 7, 8. Chapter 2. Sections 1, 2, 3, 8, 9. (sections 8. 9 overlaps with
se
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Math111 L2: Linear Algebra, Midterm Test 2
Dept of Math, HKUST, Spring 2006
Name:
ID No.:
Problem
Score
1 (20)
2 (15)
3 (20)
4 (20)
5 (25)
Total (100 pts)
1. (5+7+8 pts) Find the bases for the vector
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
HKUST
MATHlll Linear Algebra
Midterm Examination Name:
25th March 2010 Student I.D.:
9:001 0:203m
Directions:
0 DO NOT open the exam until instructed to do so.
In Please write your Name and ID numbe
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
OLD MATH111 MIDTERM EXAMS AND ANSWERS
Note1: The answers are not guaranteed to be correct. Please report any mistakes to me
Note2: The old midterm exams may cover dierent materials. Not all the past p
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Chapter4
Subspace H of V
1. Zero vector of V is in H
2. H is closed under vector addition, i.e. for each u, v in H, u+v is in H
3. H is closed under scalar multiplication,i.e. for each u in H, each sc
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
HKUST MATH2121 Linear Algebra (Spring 2016)
Final Examination
Name:
Student I.D.:
25 MAY 2016 12:30pm3:00pm
DIRECTIONS:
Question No.
Do NOT open the exam until instructed to do
so.
All mobile phones
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
FINAL EXAM MATH111 Linear Algebra Spring 2010
There are 5 problems.
Show the working steps of your answers for full credits.
3
2
1
1. (25 points) Let vectors u 1 , v 1 1 , and v 2 2 .
4
0
2
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
INFORMATION OF MATH 2121 FINAL
The final exam will cover the following sections: Chapter 1. Section 1,2,3,4,5,7,8,9.
Chapter 2. Sections 1,2,3. Chapter 3. Sections 1,2. Chapter 4. Sections 1,2,3,4,5,6
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Math 2121 Linear Algebra, 2015 Fall
Items of Course Outlines
1. Instructor (L1,L2) Chang, HuaiLiang, Rm3990, [email protected]
2. Teaching Assistant (s)  Name and Contact Details
T1a, T1b: Zhang Meng
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
HOMEWORK
Due time: 2015 Nov 2rd 4pm;
Put the writing of proofs(with name,ID,section) in the homework box math 2121
in front of math department office (Lift 25/26).
(1) (8pts) Given subsapces H and K o
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
MATH 2121 Linear algebra (Fall 2017)
1
Lecture 24
Last time: symmetric matrices
A matrix A is symmetric if AT = A.
This happens if and only if A is square and Aij = Aji for all i, j.
1 2
1 2
Example.
The Hong Kong University of Science and Technology
Linear Algebra
MATH 2121

Fall 2014
Math 2121 Linear Algebra, 2016 Fall
Items of Course Outlines
1. Instructor (L1,L2) Chang, HuaiLiang, Rm3490, mahlchang[email protected]
2. Teaching Assistant (s)  Name and Contact Details
T1A, T1B: Cheung Ho