FIRST EXAMSTUDY COPY
MATH 211, FALL 2006, WILLIAMS COLLEGE,
OCTOBER 11, 2006
These are the problems from the rst midterm exam.
1. Problem One
Compute the determinant of the matrix
1
0
A=
2
0
0 2 0
3 0 5
.
0 1 0
7 0 1
2. Problem Two
Consider the following
HOMEWORK ASSIGNMENT # 1
MATH 211, FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions to the rst homework.
1. Problem One
Describe, in your own words, the geometric way to multiply complex
numbers. Draw pictures and explain in full s
Second Exam
Math 211, Williams College
November 10, 2006
Directions: This Exam has 4 questions. Be sure to show
all of your work and explain yourself carefully. You have
two and a half hours to complete this exam, to be done
in a single block of time. You
SECOND EXAM SOLUTIONS
MATH 211, WILLIAMS COLLEGE, FALL 2006
Abstract. These are the instructors solutions for the second exam. For
statements of the problems, see the posted copy of the exam.
1. Problem One
To see if W1 and W2 are the same, we apply the r
Final Exam
Math 211, Williams College
December 15, 2006
Print your name here:
Directions: This Exam has 6 questions on 8 pages, including this cover. Be sure to show all of your work. You
have two and a half hours to complete this exam. Please
sign the ho
HOMEWORK ASSIGNMENT SOLUTIONS# 2
MATH 211, FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions for assignment 2.
1. Problem One
Use the elimination/back-solving algorithm to solve the following
systems. (i.e. put the system in row ec
HOMEWORK ASSIGNMENT # 3
MATH 211, FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions.
1. Problem: On LU decompositions
This problem will lead you through understanding the LU decomposition
of a matrix. Your answer for this problem s
MATH 211 HOMEWORK ASSIGNMENT 8
FALL 2006, WILLIAMS COLLEGE
Abstract. This assignment has 6 problems on 2 pages. It is due Wednesday,
November 21 by 5pm. Dont hesitate to ask for help. This may seem long,
but it is important to do this stu now, and not aft
HOMEWORK ASSIGNMENT # 5
MATH 211, FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions.
1. Vector Spaces and Subspaces
(1) Show directly that the set V of real valued continuous functions on the
interval [0, 1] is a vector space under
MATH 211 HOMEWORK ASSIGNMENT 7 SOLUTIONS
FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions.
1. Nonsingularity
Show that the composition of two nonsingular linear transformations is also
nonsingular.
1.1. Solution. A linear transfor
HOMEWORK ASSIGNMENT # 4
MATH 211, FALL 2006, WILLIAMS COLLEGE
Abstract. These are the instructors solutions.
1. Problem: Cofactors and Cramers rule
(1) Use the classical adjoint method
2
A = 4
6
(2) Use Cramers rule to
x1
x1
x1
to compute the inverse of