1 of 38
Linear Algebra Homework 2
Hoon Hong
LU Decomposition (LUD)
LU decomposition of A
A=
2 K
1
K K
4 1
1. Forward eliminate
2 K
1
0 K
3
,
R2 C2 R1
2. Build L and U
L=
1 0
K 1
2
,U=
1
2 K
0 K
3
2 of 38
LU decomposition of A
A=
3
4
K K
6 10
1. Forward el
MA 405 - 002: Introduction to Linear Algebra
Homework 6
October 15
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clear
MA 405 - 002: Introduction to Linear Algebra
Homework 7
November 6
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clear
MA 405: Introduction to Linear Algebra
September 10
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clearly and
succinct
MA 405 - 002: Introduction to Linear Algebra
Homework 4
September 29
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution cle
MA 405 - 002: Introduction to Linear Algebra
Homework 8
November 12
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clea
MA 405-002 Spring 2014
Jacob Norton
Test #2 - February 24, 2014
Answer the questions on your own paper. The correct answer without any work receives no credit. If we cant
nd the work or answer easily then we cant grade it; show all your work in an easy to
MA 405-002 Spring 2014
Jacob Norton
Test #1 - February 3, 2014
Answer the questions on your own paper. The correct answer without any work receives no credit. If we cant
nd the work or answer easily then we cant grade it; show all your work in an easy to
MA 405-002 Spring 2014
Jacob Norton
Quiz #9 - April 2, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Is the followi
MA 405-002 Spring 2014
Jacob Norton
Quiz #8 - March 19, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Consider the
MA 405-002 Spring 2014
Jacob Norton
Quiz #6 - February 28, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (NO points) (This quiz
MA 405-002 Spring 2014
Jacob Norton
Quiz #3 - January 24, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Consider th
MA 405-002 Spring 2014
Jacob Norton
Quiz #7 - March 7, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Determine whet
MA 405-002 Spring 2014
Jacob Norton
Quiz #5 - February 19, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Use Cramer
MA 405-002 Spring 2014
Jacob Norton
Quiz #4 - February 7, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
PRINT YOUR NAME:
1. (10 points) Conside
MA 405-002 Spring 2014
Jacob Norton
Quiz #1 - January 10, 2014
Answer the questions in the space provided on the page. Show all your work; the correct answer without any
work receives no credit. Keep your work neat!
SOLUTION KEY
1. (10 points) Solve the f
MA 405 - 002: Introduction to Linear Algebra
Practice problems
October 20, 2015
1
Study guide
Important topics
Vector spaces and subspaces
Definitions, properties and determining whether it is a subspace or not.
Span and spanning set
Knowing what the
MA 405: Introduction to Linear Algebra
Homework 1 (30 pts)
August 27, 2015
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your soluti
MA 405 - 002: Introduction to Linear Algebra
Homework 8
November 12
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clea
1 of 7
Test 3
1
Find the best approximate solution of
2
1
using Cholesky
3
K K ,b=
3 1
A=
A x = b
1 K
4
K
3
K
3
1. Compute S = At A
14
S=
1
1 18
2. Cholesky Decomposition
3.742
L=
0
0.267 4.234
3. Cholesky-based formula for the best approximate solution
3
Test 2
1
LU decomposition of A
K
4
2
A=
4
4
9 K
12
8 13
K
2
1. Forward eliminate
2
4 K
4
0
1 K ,
4
0 K 14
3
R2 K2 R1
R3 K4 R1
2 4 K
4
0 1 K ,
4
0 0
R3 C3 R2
2
2. Build L and U
1
L=
0 0
2 4 K
4
2
1 0 ,U=
0 1 K
4
3
4 K 1
0 0
2
Cholesky decomposition of S
4
Test 1
1
Solve
A x = b
using Gauss-Jordan
K
3
0
K
6
A=
3 K
3
3 K ,b=
5
0
K K K
6 3 4
K
3
1. Augment
K
3
3 K
3
0
K
6
3 K
5
0
K K K K
6 3 4 3
2. Forward eliminate
K
3
3 K
3
0
3
0 K
1
0 K
9
2 K
3
K
3
3 K
3
0 K
3
0
1
0 ,
R2 K2 R1
R3 K2 R1
0
0 ,
1 3
0 K K
R3 K
MA 405 - 002: Introduction to Linear Algebra/ Homework 3 Solutions
September 21, 2015
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of
MA 405 - 002: Introduction to Linear Algebra
September 3, 2015
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clearly a
MA 405 - 002: Introduction to Linear Algebra
Study Guide
November 20, 2015
Important topics (Sections 5.3-5.6, 6.1-6.3 of text)
Setting up the least squares problem minx kAx bk2 . Identifying A, b and x for line fitting
Solving the normal equations AT A
MA 405 - 002: Introduction to Linear Algebra
Homework 3
September 10
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution cle
MA 405 - 002: Introduction to Linear Algebra
Homework 5
October 6
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clearl
MA 405 - 002: Introduction to Linear Algebra
Homework 6
October 15
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clear
MA 405 - 002: Introduction to Linear Algebra
Practice problems
September 17, 2015
1
Study guide
Important topics
Solving systems of linear equations and reduced row echelon form
Matrix Multiplication - different ways of multiplying
Inner Products, Oute
MA 405 - 002: Introduction to Linear Algebra
Homework 7
November 6
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution clear
MA 405 - 002: Introduction to Linear Algebra
Homework 4
September 29
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solution cle
MA 405 - 002: Introduction to Linear Algebra
Homework 2 solutions
September 10
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your so
MA 405 - 002: Introduction to Linear Algebra
Study Guide
December 6, 2015
Consult previous study guides.
Complex inner products and Hermitian matrices. Section 6.4
Properties of symmetric matrices (real eigenvalues and orthogonal eigenvectors correspon
MA 405 - 002: Introduction to Linear Algebra
Homework 5 Solutions
October 6
Instructions: You are encouraged to collaborate with other students. However you must write
your own solutions and list the names of collaborators. Explain the steps of your solut