ENGG1410 Midterm (105 minutes)
No calculators allowed. Double-sided HANDWRITTEN A4 sized cheat-sheet allowed.
Cheating will be dealt with severely.
Name:
Student ID:
1. Let f (x, y) = x2 + y 2 2x + 4y + 10.
(a) (4 points) Find the point where f , the grad

Linear Algebra
Done Wrong
Sergei Treil
Department of Mathematics, Brown University
Copyright c Sergei Treil, 2004, 2009, 2011, 2014
Preface
The title of the book sounds a bit mysterious. Why should anyone read this
book if it presents the subject in a wro

ENGG1410 Linear Algebra and Vector Calculus
Homework Assignment 2
Due: Feb 13, 2017
1. Solve the following linear equations:
3 x1 6 x 2 3 x 4 3 x5 2 x6 7
x1 2 x 2 x 4 x5 1
x3 x 4 2 x 5 x 6 0
2 x1 4 x 2 2 x3 4 x 4 6 x5 5 x6 4
Specifically solve for the sol

Prof. Zhuoyu Long
ENGG 1410A
Spring 2015
Homework 6
DUE DAY: 14 April (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem 7.7-12, 13
Evaluate the following determinants and show details.
0
4
a b c
4

1. A vector space S is spanned by vectors [3, 6, 0] , [3, 9, 3] , and [9, 3, 3] .
(a) Determine the dimension of space S.
(b) Find a basis of vector space S.
(c) Determine whether the vector [3, 0, 3] lies in S.
1
2. Show that the vector space spanned by

THE CHINESE UNIVERSITY OF HONG KONG
Department of Mathematics
MATH1510 Calculus for Engineers (Fall 2016)
Homework 4
Due Date: November 16, 2016
Name:
Student No.:
Class:
Final Result:
I acknowledge that I am aware of University policy and regulations on

Prof. Zhuoyu Long
ENGG 1410E
Homework 6
DUE DAY: 20 April (Wed)
SUBMISSION: Put it in the ENGG1410E mailbox on the 5th floor of ERB Building
Questions:
1. Problem 7.7-12, 13
Evaluate the following determinants and show details.
0
4
a b c
4 0
c a b ,

Prof. Zhuoyu Long
ENGG 1410E
Homework 5
DUE DAY: 6 Apr (Wed)
SUBMISSION: Put it in the ENGG1410E mailbox on the 5th floor of ERB Building
Questions:
1. Problem 7.2-7
Idempotent matrix, defined by A2 = A. Can you find four 2 2 idempotent matrices?
2. Probl

Solution to Homework 5
1. Problem 7.2-7
a b
If a matrix
is idempotent, then
c d
2 2
a b
a + bc ab + bd
a b
=
=
.
c d
ac + dc bc + d2
c d
Hence any matrix that satisfies the following four
2
a + bc
ab + bd
ac + dc
bc + d2
equations is an idempotent mat

Prof. Zhuoyu Long
ENGG 1410A
Homework 4
DUE DAY: 17 Mar (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem 10.6-4
Evaluate the integral for the given data. Describe the kind of surface. Show the
detail

Prof. Zhuoyu Long
ENGG 1410A Spring 2015
Homework 7
Due date: No Submission
1. Problem 8.1-11
Eigenvalues, eigenvectors. Find the eigenvalues. Find the corresponding
eigenvectors for all rather than just = 4.
4 2 2
2 5 0
2 0 3
2. Problem 8.1-24
Inverse ma

Prof. Zhuoyu Long
ENGG 1410A
Homework 2
DUE DAY: 10 Feb (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem 9.5-13
Find a parametric representation of the straight line through (3, 1, 2) in the directio

ENGG1410C Linear Algebra and Vector Calculus
Homework Assignment 4
Due: March 27, 2017
1. Given vectors a and b, with a=[2, 1, 2], b=[1, 1, 0], find
a) the angle between the two vectors.
b) the component of b along the direction of a, and the component of

ENGG1410 Linear Algebra and Vector Calculus
Homework Assignment 1
Due: Jan 27, 2017
1. Consider the encryption example in classnotes (Section 7.2). Use the same code for the
alphabets and space, i.e.,
3 3 4
1
1 as the example. Generate the encrypted
and

ENGG1410E: Linear Algebra & Vector Calculus for Engineers
Spring Term 2017
Assignment 1
Due date: Feb 10, 2017, 6:30pm
Important notes:
1. Please submit your assignment on time. No late assignment will be accepted.
2. Please drop your assignment into the

ENGG1410E: Linear Algebra & Vector Calculus for Engineers
Spring Term 2017
Assignment 2
Due date: Mar 10, 2017, 6:30pm
Important notes:
1. Please submit your assignment on time. No late assignment will be accepted.
2. Please drop your assignment into the

Lecture Notes: Line (Curve) Integral by Length
Yufei Tao
Department of Computer Science and Engineering
Chinese University of Hong Kong
[email protected]
1
Length of a Curve
Recall that we can represent a curve in Rd using a vector function r(t) = [x1

Prof. Zhuoyu Long
ENGG 1410A
Homework 5
DUE DAY: 31 Mar (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem 7.2-7
Idempotent matrix, defined by A2 = A. Can you find four 2 2 idempotent matrices?
2. Prob

Prof. Zhuoyu Long
ENGG 1410A Spring 2015
Homework 1
January 13, 2015
DUE DAY: 27 Jan (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem 9.1-4
Find the components of the vector v with initial point P :

Prof. Zhuoyu Long
ENGG 1410A
Homework 3
DUE DAY: 3 Mar (Tue)
SUBMISSION: Put it in the ENGG1410A mailbox on the 5th floor of ERB Building
Questions:
1. Problem R10.1-5
Calculate C F(r) dr for the given data. If F is a force, this gives the work done
by th

Prof. Daniel Zhuoyu Long
ENGG 1410E
Homework 4
DUE DAY: 23 Mar (Wed)
SUBMISSION: Put it in the ENGG1410E mailbox on the 5th floor of ERB Building
Questions:
1. Problem 10.5-5
Familiarize yourself with parametric representations of important surfaces by dr

Department of System Engineering and
Engineering Management ENGG1410E
2015-2016 Term 2
Solution 4
Solution 1.
Parametric representation of z = f (x, y) is
x2 + y 2 = u2 , z = u2
Parameter curve u = u0 and v = v0 for r(u, v) = [ucosv, usinv, u2 ]:
r(u0 , v

Prof. Zhuoyu Long
ENGG 1410E Spring 2016
Homework 7
Due date: No Submission
1. Problem 8.1-11
Eigenvalues, eigenvectors. Find the eigenvalues. Find the corresponding
eigenvectors for all rather than just = 4.
4 2 2
2 5 0
2 0 3
2. Problem 8.1-24
Inverse ma

l
H wiWWL \ go (Mt? 0
V : cfw_>61 : (L43 2) 0,452) : [-3] g _+]
vz=m-
~ lgq. =1 2J1,
_ v D N
u _ 2, 8, +3 i.
I 25, l V" I ' M J
7 : P& .5 &
(~3+5, l+l;"+63>)
(0) 0) 4')
K [-3, 2, I]
W hr-1 dorm a Twat-F (Mend E cfw_$.-
F-q-C: [5,z,|]+ [110,5] : [4,125

ENGG1410D: Linear Algebra and Vector Calculus for Engineers
Spring 2017
Assignment 6
Due date: April 11, 2017, 7:00pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment into t

ENGG1410D: Linear Algebra and Vector Calculus for Engineers
Spring 2017
Assignment 8
Due date: April 26, 2017, 7:00pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment into t

ENGG1410D: Linear Algebra and Vector Calculus for Engineers
Spring 2017
Assignment 7
Due date: April 20, 2017, 7:00pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment into t

ENGG1410D: Linear Algebra and Vector Calculus for Engineers
Spring 2017
Assignment 2
Due date: February 21, 2017, 7:00pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment int

ENGG1410D: Linear Algebra and Vector Calculus for Engineers
Spring 2017
Assignment 3
Due date: February 28, 2017, 7:00pm
Important notes:
1. You must submit your assignment on time. No late assignment will be accepted.
2. You must drop your assignment int