MATH2014 Multivariable Calculus and Linear Algebra
Brief Solution to Assignment 1
1. Show that for every real number k, the plane
(x 2y + z + 3) + k(2x y z + 1) = 0
contains the line of intersection of the planes
x 2y + z + 3 = 0 and 2x y z + 1 = 0.
Solut
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 2
Instructions
- Due date: 5:00 p.m., 14 October, 2016
- Write on white A4 paper. Staple multi-page assignments in the top left corner only.
Dont put your assignment in a plastic folder.
- Writ
Rutgers University Press
Chapter Title: MORE THAN HOMOPHOBIA: The Race, Class, and Gender Dynamics of AntiLGBT Violence
Book Title: Violence against Queer People
Book Subtitle: Race, Class, Gender, and the Persistence of Anti-LGBT Discrimination
Book Auth
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 3
1. Show that the only possible maxima and minima of z on the surface z = x3 + y 3 9xy + 27
occur at (0, 0) and (3, 3). Show that neither a maximum nor a minimum occurs at (0, 0).
Determine wh
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 10
1. Consider a linear system whose augmented matrix is of the form
1 2 1 0
2 5 3 0 .
1 1 0
(a) Is it possible for the system to be inconsistent? Explain.
(b) For what values of will the
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 9
1. Use back substitution to solve each of the system
x1 +
x2 +
2x2 +
x3 = 8
x3 = 5 .
3x3 = 9
2. Write out the system of equations that corresponds to the following augmented matrices:
3 2
T1/MATH2014/2016-17/1st
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Tutorial 1
Date : Sep 19, 2016 Sep 23, 2016
1. Let f (x, y) =
2x3y
x+y ,
where x + y 6= 0. Show that
lim
f (x, y)
(x,y)(0,0)
d
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 2
Instructions
- Due date: 5:00 p.m., 18 March, 2016
- Write on white A4 paper; use one side only. Staple multi-page assignments in the top
left corner only. Dont put your assignment in a plast
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 2
1. Let
sin(x y) ,
|x| + |y|
f (x, y) =
0,
(x, y) = (0, 0)
(x, y) = (0, 0).
Is f continuous at the origin? Why?
Solution. Along the half-line y = 0, x > 0, lim(x,y)(0,0) f (x, y) = 1 = f (0,
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 5
1. Find the volume of the region enclosed by the spherical coordinate surface = 2 sin .
2 2 sin
Solution. V =
2 sin ddd = 2 2
0
0
0
2. A circular cylindrical hole is bored through a solid s
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 4
1. In the following exercises, sketch the region of integration and evaluate the double integral.
10
1/y
xy
(a)
ye dxdy
1
1
(b)
0
2 y
xy dxdy
y
0
Solution.
(a) 9(e 1)
(b) 1/5
2. In the follow
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 6
1. Find the eigenvalues and the corresponding eigenspaces for each of the following matrices.
(
)
2 0
1
3 2
(a)
(b) 1 0 1
4 1
0 1 1
Solution.
(a) Two eigenvalues 5 and 1. The eigenspace corr
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 11
1. Let
3
2 4
A = 1 2 3 .
2
3 2
(a) Find the values of det(M21 ), det(M22 ) and det(M23 ).
(b) Find the values of A21 , A22 and A23 .
(c) Use your answers from part (b) to compute det(A).
Math2014 Multivariable calculus and linear algebra
ZHANG Haiyu Doris
The University of Hong Kong
hyzhang@maths.hku.hk
January 12, 2016
ZHANG Haiyu Doris (HKU)
Math2014
January 12, 2016
1 / 51
Table of Contents
Part I: Multivariable calculus
Chapter 1 Part
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 5
Instructions
- Due date: 5:00 p.m., 29 April, 2016
- Write on white A4 paper. Staple multi-page assignments in the top left corner only.
Dont put your assignment in a plastic folder.
- Write
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 1
Instructions
- Due date: 5:00 p.m., 26 Feb, 2016
- Write on A4 size paper. Staple multi-page assignments in the top left corner only.
Dont put your assignment in a plastic folder.
- Write you
Math2014 Chapter 3
Linear Algebra
1
2
3
4
Example 1
5
6
7
8
9
10
Row Reduction and Echelon Forms
A rectangular matrix is in echelon form (or row
echelon form) if it has the following three
properties:
1. All nonzero rows are above any rows of all
zeros.
2
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 4
Instructions
- Due date: 5:00 p.m., 15 April, 2016
- Write on white A4 paper. Staple multi-page assignments in the top left corner only.
Dont put your assignment in a plastic folder.
- Write
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 3
Instructions
- Due date: 5:00 p.m., 1 April, 2016
- Write on white A4 paper; use one side only. Staple multi-page assignments in the top
left corner only. Dont put your assignment in a plasti
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 11
1. Let
3
2 4
A = 1 2 3 .
2
3 2
(a) Find the values of det(M21 ), det(M22 ) and det(M23 ).
(b) Find the values of A21 , A22 and A23 .
(c) Use your answers from part (b) to compute det(A).