Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Final Exam, Fall 2014
This is a closed book, closed notes exam. You need to justify every one
of your
a
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Math 113, Section 5
Homework #5
Fall 2017
Exercises 8: 43, 47, 49
Exercises 9: 29, 33, 34, 36
Exercises 13: 2, 16, 17, 50
Additional exercises:
1. Let : G G0 be a homomorphism. Prove each of the follo
Math H54
Homework #3
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N
Math 113, Section 5
Homework #1
Fall 2017
Exercises 4: 3, 5, 6, 19, 29, 31, 32, 36, 37
Additional exercises:
1. Prove that the identity element of a group is unique. (This justifies the use of
the spe
Math H54
Homework #6
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N
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Math H54
Homework #7
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N
Math H54
Homework #4
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N
W
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2
Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Sample Final, Fall 2014
This is a closed book, closed notes exam. You need to justify every one
of you
Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Solution to Sample Midterm
II, Fall 2014
This is a closed book, closed notes exam. You need to justify
Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Solution to Sample Midterm
II, Fall 2014
This is a closed book, closed notes exam. You need to justify
Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Sample Midterm I, Fall 2014
This is a closed book, closed notes exam. You need to justify every one
of
Lin Lin, Evans 1083
Email: [email protected]
http:/math.berkeley.edu/~linlin/H54
Math H54: Sample Midterm II, Fall 2014
This is a closed book, closed notes exam. You need to justify every one
o
MATLAB code for plotting convergence of Fourier series
% Step function
N=100;
x=(-pi+(0:N-1)*(2*pi)/N)';
fx=zeros(size(x);
fx(find(x<0)=-1;
fx(find(x>=0)=1;
M=3*N;
xext=(-3*pi+(0:M-1)*(6*pi)/M)';
fext
1. Determinant is the product of eigenvalues. Let A be an n n matrix, and let (A) be its
characteristic polynomial, and let 1 , . . . , n be the roots of (A) counted with multiplicity. Show that
det(A
Let V be the vector space consisting of all two by two matrices, and W be the vector space consisting
of one by one matrices. Dene
1
T (X) = 1 2 X
1
1.
2.
3.
4.
5.
Find a basis for V and W , and compu
W
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Math 113 Section 5
September 19, 2017
Quiz 1
You have 30 minutes to complete the quiz. I will give you 10, 5, and 1 minute
warnings.
There are 4 problems worth 10 points each, for a total of 40 poin
Bijection between R3 and R2
How can we find a bijection g : R3 R2 ? First, note that it is enough to find a
bijection f : R2 R, since then g(x, y, z) = f (f (x, y), z) is automatically a bijection
fro
Math H54 First Midterm
Wed 5 Oct 2015, 10:1011:00 AM
Your Name:
Instructions
EXAM SCORES
(1). Check that you have all 6 pages of this
exam booklet.
(2). Be sure to show all your steps. In particular,
Math H54 Midterm 1
September 20, 2010
Professor Michael VanValkenburgh
Name:
Student ID:
Instructions: Show all of your work, and clearly indicate your answers. Use the backs of pages as scratch
paper
Math H54
Homework #1
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N
Math H54
Midterm Questions
Fall 2017
1. Suppose cfw_ #
v 1 , #
v 2 is a linearly independent set in Rn . Show that cfw_ #
v 1 , #
v 1 + #
v 2
is also linearly independent.
2. Let M be the 3 3 matrix
Math H54
Homework #5
Fall 2017
The following exercises are from the corresponding sections of the UC Berkeley
custom edition of Lay, Nagle, Saff, & Snider, Linear Algebra and Differential Equations. N