MATH 531
Written Homework 1 Solution
Radford
10/17/07
1. (20 points)
(a) (3) First note that a2 = 0 for all a A implies ab = ba for all a, b A as
0 = (a + b)2 = a2 + ab + ba + b2 = ab + ba.
Thus
J (a, a, b) = a(ab) + a(ba) + b(aa) = a(ab) + a(ab) + a(0) =
ENG102A: LIT/COMP LAC I (ELI-PUBLISHABLE) | Unit 1 : Paragraph | Lesson 5
Student Guide
Lesson 5: Planning a Paragraph
You have been studying the elements of an effective paragraph. Now you will review the writing process and plan
a paragraph of your own.
Math | Graded Assignment | Unit Test, Part 2 | Systems of Equations
Name:
Date:
Graded Assignment
Unit Test, Part 2: Systems of Equations
Show all your work.
(10 points)
1.
At a fundraiser breakfast, the bill for 3 glasses of orange juice and 5 pancake sp
ENG102A: LIT/COMP LAC I (ELI-PUBLISHABLE) | Unit 1 : Paragraph | Lesson 2
Student Guide
Lesson 2: Parts of a Paragraph
Not all paragraphs are exactly the same, but all good paragraphs have certain components. An effective
paragraph begins with a topic sen
Graded AssignmentMTH122A: Algebra I | Unit 7 | Lesson 16: Linear Equations and Inequalities Unit Test
Name:
Date:
Graded Assignment
Unit Test, Part 2
Show all your work.
(6 points)
1.
Using the slope-intercept form of a line, find the equation of the line
Math | Graded Assignment | Unit Test, Part 2 | Systems of Equations
Name:
Date:
Graded Assignment
Unit Test, Part 2: Systems of Equations
Show all your work.
(10 points)
1.
At a fundraiser breakfast, the bill for 3 glasses of orange juice and 5 pancake sp
ENG102A: Literary Analysis and Composition I | Unit 1 | Lesson 4: Paragraph Conventions
Self-Check Answers
Review and Practice
1. Draw a line to match each item with its definition.
unity b. All sentences support the main idea.
transitions a. Words or phr
Math | Graded Assignment | Unit Test, Part 2 | Applying Fractions
Name:
Date:
Graded Assignment
Unit Test, Part 2: Applying Fractions
Show all your work.
(7 points)
1.
Set up the following word problem as an equation and solve. Then write your answer as
a
MATH 531
Notes on Simple sl (2, F )-modules
Radford 11/09/07
Throughout F is an algebraically closed eld of characteristic zero. Let F and Z () be
the vector space over F with basis cfw_v Z . We dene endomorphisms x, y, h of Z () by
x(v ) = ( + 1)v
for a
MATH 531
Written Homework 3 Solution
Radford
11/05/07
In the following exercises F is a eld, algebraically closed and of characteristic zero. We
follow the notation of the text and that used in class.
1. (25 points) You may assume that L = L1 Lr is an alg
MATH 531
Radford 01/14/03, revised 02/08/03, 09/06/07
Decomposition of Operators
Throughout V is a nite-dimensional vector space over a eld F and T is a linear endomorphism of V . Recall that A = End(V ) is an associative algebra with unity IV over F unde
MATH 531
Written Homework 5 Solution
Radford
11/20/07
We follow the notation of the text and that used in class. You may use results from
the course materials on the class homepage and the text. This version replaces the
previous one.
1. (35 points) Lk, =
MATH 531
Written Homework 4 Solution
Radford
11/21/07
In this exercise set we begin a rather detailed study of sl (n, F ).
1. (20 points) For all 1 i, j, k, n note ei j ek = j,k ei ; thus [ei j ek ] = j,k ei ,i ek j .
(a) (5) This is boring but necessary.
MATH 531
Written Homework 2 Solution
Radford
10/18/07
1. (20 points) A is a Lie algebra over F , S is a subspace of L, S (0) , S (1) , S (2) , . . . dened
inductively by S (0) = S and S (i+1) = [S (i) S (i) ] for i 0.
(a) (4) (S (i) )(j ) = S (i+j ) for a
ENG102A: LIT/COMP LAC I (ELI-PUBLISHABLE) | Unit 1 : Paragraph | Lesson 3
Student Guide
Lesson 3: Paragraph Decisions
In this lesson, you will learn about some of the important decisions writers make in writing effective paragraphs.
Lesson Objectives
Ide