CSci 2033, F12
Homework # 6
Due Date: 12/10/2012
1. The yearly temperature cycle in Fairbanks, Alaska is given in the next table.
Date
abc d
e
fgh
i
jk
lm
Degrees -14 -9 2 15 35 52 62 63 58 50 34 12 -5
There are 13 equally spaced data points which corresp
Assignment #2: Vector and Matrix Equations, Solution Sets of Linear Systems, and
Applications
Due date: Monday, February 9, 2015 (4:00pm)
Name: _
Section Number
Assignment #2: Vector and Matrix Equations, Solution Sets of Linear Systems, and
Applications
CSci 2033 - Practice Midterm #2 Answer Key
1. (X A)B = BC,
(X A) BB 1 = BCB 1 . Both sides right-multiplied by B1 .
I
1
X A = BCB , and so X = BCB 1 + A.
2 6
14 4 18
0
3 12 6
3
. Further row reduction of U is not needed. For L, copy the
2. Take U =
0
Assignment 1
Due:
Fri Sep 25 2015 09:05 AM CDT
Description
The questions in this assignment are are taken from or similar to the questions in
Sections 1.1-1.4 of the textbook.
Instructions
This assignment is due Friday, September 25 at the beginning of le
Assignment #8: Diagonalization, Applications, Iterative Estimates of Eigenvalues/Eigenvectors
Due date: Monday, April 13, 2015 (4:00pm)
Name: _
Section Number
Assignment #8: Diagonalization, Applications, Iterative Estimates of Eigenvalues/Eigenvectors
Du
Assignment #4: Introduction to Matrix Operations and the Inverse of a Matrix
Due date: Monday, March 3, 2015 (4:00pm)
Name: _
Section Number
Assignment #4: Introduction to Matrix Operations and the Inverse of a Matrix
Due date: Monday, March 3, 2015 (4:00
Assignment #5: Partitioned Matrices, Matrix Factorizations, and Applications to Economic
Models and Computer Graphics
Due date: Monday, March 9, 2015 (4:00pm)
Name: _
Section Number
Assignment #5: Partitioned Matrices, Matrix Factorizations, and Applicati
Assignment #7: Determinants, Eigenvalues, and Eigenvectors
Due date: Monday, April 6, 2015 (4:00pm)
Name: _
Section Number
Assignment #7: Determinants, Eigenvalues, and Eigenvectors
Due date: Monday, April 6, 2015 (4:00pm)
For full credit you must show al
Assignment #6: Subspaces, Bases, Dimension and Rank
Due date: Monday, March 23, 2015 (4:00pm)
Name: _
Section Number
Assignment #6: Subspaces, Bases, Dimension and Rank
Monday, March 23, 2015 (4:00pm)
For full credit you must show all of your work.
1. In
Assignment #3: Linear Independence, Linear Transformations and Linear Models,
Applications
Due date: Monday, February 16, 2015 (4:00pm)
Name: _
Section Number
Assignment #3: Linear Independence, Linear Transformations and Linear Models, Applications
Due d
Assignment #1: Number Representation on a Computer, Loss of Precision, Systems of
Linear Equations, Echelon Form
Due date: Monday, February 2, 2015 (4:00pm)
Name: _
Section Number
Assignment #1: Number Representation on a Computer, Loss of Precision, Syst
CSci 2033, F12
Quiz 4
November 28, 2012
Do work together to nd answers to the questions. You may be called and asked to give
your answer to a specic question.
1. Let v1, v2, in Rm. Show that H = spancfw_v1, v2
is a subspace of Rm.
2. What is the dimension
CSci 2033, F12
Quiz # 1
Today: Sept. 24, 2012
Name:
The rules: You can and are encouraged to discuss answers to the questions. You need to
write your own anwser at the end of the discussion phase. You will get credit for this quizz
if you have written an
Eigenvalue Problems. Introduction
Let A an n n real nonsymmetric matrix. The eigenvalue
problem:
C : eigenvalue
u Cn : eigenvector
Au = u
EIGENVALE PROBLEMS AND THE SVD. [5.1 TO 5.3 & 7.4]
Example:
A=
20
21
1 = 1 with eigenvector u1 =
0
1
2 = 2 with ei
Orthogonality The Gram-Schmidt algorithm
1. Two vectors u and v are orthogonal if u.v = 0.
2. They are orthonormal if in addition u = v = 1
3. In this case the matrix Q = [u, v ] is such
QT Q = I
THE GRAM-SCHMIDT ALGORITHM AND QR [6.4]
We say that the sy
CSci 2033 - Example Midterm #1 Questions
1. Determine which of the following sets of vectors are linearly independent. Give reasons for your answers.
6
2
1
3
4
3
a.
,
,
,
b. 12 , 4
4
9
12
7
3
1
1
1
3
3
0
2
c. 2 , 4 , 8
d. 12 , 0 , 9
1
3
2
3
0
CSci 2033 - Example Midterm #1 Questions - Answer Key
1. a. Linearly dependent because there are more vectors than entries in the vectors.
b. Linearly dependent because the second vector is 1/3 times the rst vector.
c. We may study Ax = 0 to determine if
CSci 2033 - Practice Midterm #2
1. Solve the matrix equation (X A)B = BC for X, assuming that the matrices A, B, and C are invertible.
2. Suppose that a matrix A has been reduced to
2
2 6
14 4
18
1
6 19 4
6 0
A=
2
7 18 1 11 0
0
3 8
17 3
18
2 6
14 4 1
CSci 2033 - Practice Final
In addition to these example questions from material covered since the last midterm, there will also be
questions similar to those that appeared on the first two midterms.
1. Find a, b, and c for which the matrix
a
b
A=
c
1
2
1
CSci 2033 - Practice Final Answer Key
1. Solve AT A = I for a, b, and c. The only
1
c = 3 .
1 1
1 2 3
5 , AT A =
2. A = 2
1 5 4
3
4
2
possibilities are a = 0, b = 6 , c =
1
5 =
4
1
2
3
14
21
21
42
1
3
or a = 0, b =
2
,
6
,
AT b =
Solving AT Ax = AT b,
1
Assignment 6
Due:
Wed Dec 16 2015 09:05 AM CST
Description
The questions in this assignment are taken from or similar to the questions in Sections
4.3, 5.1 and 7.3 of the textbook.
Instructions
This assignment is due Wednesday, December 16 at the beginnin
Assignment 3
Due: Fri Oct 30 2015 09:05 AM
Description
The questions in this assignment are taken from or similar to the questions in Sections
3.1-3.4 of the textbook.
Instructions
This assignment is due Friday, October 30 at the beginning of lecture. You
Assignment 4
Due:
Fri Nov 13 2015 09:05 AM CST
Description
The questions in this assignment are taken from or similar to the questions in Sections
3.5-3.7 of the textbook.
Instructions
This assignment is due Friday, November 13 at the beginning of lecture
2033 HW4 Solution
Policy Note: except the situations listed under each question, any other reasonable penalty is
possible.
1.
(2 points)
Wrong answer: -2. Right answer without counterexample or explanation: -1.
An
2033 HW3 Solution
Policy Note: except the situations listed under each question, any other reasonable penalty is possible.
1.
(4 points)
At least one of the 3 intermediate steps should show up, if not -1. Calculat
2033 HW6 Solution
Policy Note: except the situations listed under each question, any other reasonable penalty is possible.
1.
(4 points)
Right answer without any steps: -2. Wrong method: -4
(2 points)
(6 points)
2 points for each eigenspace. Right answer
2033 HW5 Solution
Policy Note: except the situations listed under each question, any other reasonable penalty is
possible.
1.
(3 points)
Wrong method: -3. Right answer with calculation error: -1.
2.
(3 points
HW2 Solution
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Let the quadratic polynomial be () = 2 + + . By substituting (1,1), (2,2) (3,5) into the
equation, we get a linear system
1
1
1
1
[4] + [2] + [1] =[2]
9
3
1
5
After solving i
Assignment 2
Description
The questions in this assignment are taken from or similar to the questions in Sections
2.1-2.5 in the textbook.
Instructions
This assignment is due Friday, October 9 at the beginning of lecture. You must show
your work in order t