AS4sol/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 4 Suggested Solution
1. (a) Let y c(A) N (A). Then y = Ax and Ay = 0. Hence, x N (A2 ).
(b) Since N (A) N (A2 ), from rank(A) = rank(A2 ),
AS4/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 4
Due date : April 20, 2011 before 6:30 p.m.
Where to hand-in : Assignment Box outside the lifts on the 4th oor of Run Run Shaw
1. Let A be a
AS3sol/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 3 Suggested Solution
1. (a) Let L be the transition matrix from F to E . By denition, we have
[v ]E = L[v ]F for any v V .
()
1
0
Set v = f
AS3/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 3
Due date : Mar 29, 2012
before 6:30 p.m.
Where to hand-in : Assignment Box outside the lifts on the 4th oor of Run Run Shaw
Remember : Plagi
PHYS1415 General Physics II Tutorial 3 (Week of March 12-16)
1. A Van de Graaff generator is a device for generating a large electric potential by building up
charge on a hollow metal sphere. We have a demonstration unit here at HKU which has a
diameter o
PHYS 1415 General Physics II
Tutorial 1 (Week of Feb 6-10)
1. An infinite long line of charge of constant charge density 1 is located near the
line AB which carries uniform charges with charge density + 2. Suppose both two
lines are in the same plane, cal
PHYS1415 General Physics II
Laboratory Report 2: The A.C. Circuitry
Student name: _ Student No.:_
Group No.:_ Date: _
Internal resistance of the signal generator, at Output Adjust = 5
sine wave : Ri = _
square wave : Ri =_
(A) What is the value of the tim
PHYS1415 General Physics II
Laboratory 2: The A.C. Circuitry
This experiment illustrates the main properties of a simple resistance-capacitance (RC)
circuit, including the charge and discharge curves of capacitor through a resistor.
I.
RC circuit Charge a
PHYS1415 General Physics II
Laboratory Report 1
Student Name:
Ms
Student No.:
Group No.:
Date:
(A) (i) Calculate what is the sweep period now.
(ii) Check your answer by timing the sweep roughly (an ordinary watch will do)
(iii) Compare your measurement an
PHYS1415 General Physics II
Laboratory 1: Operation of a cathode ray oscilloscope (CRO)
Introduction
The cathode ray oscilloscope (CRO) is one of the most commonly used and
most useful instruments in a physics laboratory. It is conventionally an analog sy
Consider two air-filled parallel-plate capacitors of capacitance C
in series across the terminals of a battery of voltage V.
(a) What is the potential difference Vi across the plates of the
capacitors?
(b) What is the charge |qi| accumulated on each capac
(Knight Chapter 31, Problem 63) What are the current passing through
the battery Ibat and the potential difference Vab between points a
and b when the switch in the figure below is (a) open, and (b) closed?
31.63.
Model:
The battery and the connecting wir
VECTOR CALCULUS SUMMARY
LINE INTEGRAL: The notation
F dl means that at every point on
C
the curve C, evaluate the value of F dl and add up all values
from all the points on loop C by integration. The vector dl ,
(as described in lecture notes Chapter 1, P
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J3 It? t l1}
mA :d- EMA 4 Jildlf' = 3!
5 A= 41"?
A I it
6 = Can(4+?o')i+53"(?")?
n. 35 urn0
A. 1 - B A *
ar9= z+? i
Example: Vector and coordinate systems
j
Given the vector A 3i 2 k , express it in terms of cylindrical coordinates defined by the vector
A , i.e. express A a r r a a z z . You have to determine the unit vectors r , , z , expressing them in
j,
terms of
AS2sol/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 2 Suggested Solution
1. Let A = aij
nn
and B = bij
nn
. Then,
n
(a) tr(A + B ) =
n
(aii + bii ) =
n
aii +
i=1
i=1
bii = tr(A) + tr(B ).
i=1
AS1/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 1
Due date : Feb 21, 2012 before 6:30 p.m.
Where to hand-in : Assignment Box outside the lifts on the 4th oor of Run Run Shaw
Remember to writ
AS1sol/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 1 Suggested Solution
Remark: You may nd that the solutions (especially the proofs) are rather lengthy. It is because we hope to
explain eve
AS1/MATH1111/YKL/11-12
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH1111: Linear Algebra
Assignment 1
Due date : Feb 7, 2012 before 6:30 p.m.
Where to hand-in : Assignment Box outside the lifts on the 4th oor of Run Run Shaw
Remember to write
Chapter 9
Strings
A string is a sequence of characters. There are two ways to
represent strings in C+, C-style strings and string class
A C-style string stores a string in a char array. Its end is
signaled by the null character \0. A char array of size
Chapter 8
Streams and Text File I/O
a.txt
A file is a collection of data in a disk.
A text file is a file containing characters.
This chapter discuss how to read from and write to a
text file.
1
Output streams
In C+, writing to a text file is treated
Chapter 7
Arrays
An array is a collection of data of the same type. For
example, we use an array of 3 entries (each holds one int
value) to represent a vector of three integers, eg, (2, 4, 7).
An array occupies contiguous cells in RAM.
Each entry occupi
Chapter 6
Functions I
A function is a small program which accomplishes a
specific task. For example, we invoke (call) the
function, sqrt(x), in the library cmath to compute the
square root of x
#include <cmath>
int main()
cfw_
.
b = sqrt( 9.0);
.
<cmath
Chapter 5C
Modular Programming
1
Modular Programming
A module is a logically self-contained component of a
program. Each module is a function.
To develop a program for accomplishing a large task,
first decompose the task into smaller sub-tasks. Next,
wr
Chapter 5B
Iterations (Loops)
In daily life, we often do something repeatedly. Eg, we
construct a building floor by floor in the same way.
Moreover, we do something repeatedly as long as a
certain condition is satisfied. Eg, we construct a building
floo
Chapter 5A
Boolean Data Type and IF Statements
In daily life, we often do (or do not do) something,
depending on a condition. Eg,
If it rains, bring an umbrella.
If typhoon signal No. 8 is hoisted, go home.
If she knows C+, date her.
We can attach a con