Mini-Application Project
Equilibrium Temperature Distribution
Overview
A common problem encountered in thermodynamics is that of solving for the equilibrium
temperature distribution of a thin plate of metal. One way of solving this type of problem i
Justins Guide to MATLAB in MATH240 - Part 1
This Justins Guide is an edited version of a guide by Justin Wyss-Gallifent. It is instructional guide
before the actual Project 1, with information you will need to have.
Be sure also to read our MATH 240 onlin
Following Justins Guide to MATLAB in MATH240 - Part 3
1. Method
You may want to review the first two guides whilst reading this one; the assumption is that you are
comfortable with all those commands though not all are necessary.
2. New Commands
(a) Rank(
NAME MATH 240 Fall 2015 Section
Write your name and your section number on this page and each answer sheet. To receive full credit, show
work.No calculators or audio devices are allowed. You are allowed a letter size (8.51:1 1) formula sheet.
Read the ins
Justins Guide to MATLAB in MATH240 - Part 1
This Justins Guide is an edited version of a guide by Justin Wyss-Gallifent. It is instructional guide
before the actual Project 1, with information you will need to have.
Be sure also to read our MATH 240 onlin
Math 240
Section 0211/0221
11/10/2016
Section 5.4
Matrix for T relative to B: [T (x)]B = [T ]B [x]B
Section 5.5
Complex eigenvalues occur in conjugate pairs.
If A is a real 2 2 matrix with a complex eigenvalue = a bi (i =
6 0) and an associated
eigenvecto
MATLAB Project 2: MATH240, Fall 2016
1. Method
This page is more information which can be helpful for your MATLAB work, including some new
commands. Youre responsible for knowing whats been done before. The project starts on the next
page. The previous gu
%PROBLEM 4
clear all
% Suppose you want to show that [a; b] is in the span of ([-2; 1], [1; 6])
% for any a and b.
% (a) First declare a and b as symbolic (unknown constants).
syms a b
% (b) Enter a matrix A which can help you show this.
A = [-2 1 a; 1 6
project2_solutions
3/16/15, 11:57 AM
Contents
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
% Matlab Project 2
Problem 1
clear all
% (a)
A = [2 8 0 24 59; -2 -4 -6 -10 -14; 6 24 -8 96 128;10 16 48 0 70]
% (b)
R = rref(A)
MATH240. Spring 2015. MATLAB Project 2. Due March 13.
1. Method
This page is more information which can be helpful for your MATLAB work, including some new
commands. Youre responsible for knowing whats been done before. The project starts on the next
page
Matlab Project 1: SOLUTIONS
2/13/15, 3:32 PM
Matlab Project 1: SOLUTIONS
Contents
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 1
clear all
% (a) Enter the augmented matrix
A = [1 2 -3 1;-4 -5 2 -7; 2 3 -1 5]
% (b) Use elementary row
Math 240 Homework Seven
Do the following problems showing all your work. Be sure to submit your solutions in
PDF format to the Assignment area of LEO. (Point values are given in the square
brackets.)
1. [3] Determine the basis for the image and kernel of
Math 240 Homework Seven Solutions
1. [3] Determine the basis for the image and kernel of the matrix (transformation) A
given by:
4
= 3
2
1
8
6
4
2
1
1
1
3
1 6
2 5
9 10
2 0
Notice that the matrix is 54, thus the system is underdetermined and there is at
le
Math 240 Exam 1 Sample 2
1. Consider the three vectors u =
Spring 2007
2
1
1
,v=
and w =
.
1
1
1
(a) Show that u, v and w are not linearly independent using the strict denition.
(b) Explain why any pair of these vectors is linearly independent.
(c) Give a
Math 240 Exam 1 Sample 1
Spring 2008
1. Consider the following three matrices:
9 3
3 1
B=
6 2
0
0
1
101
A = 2 0 6 2
4 1 2 3
1 2 1
2 8
C = 0
4 5
9
(a) For each of A, B and C , determine if the columns are linearly independent or not.
Justify each.
(b) Fo
Math 240 Exam 3 Sample 2
Spring 2008
Please put problem 1 on answer sheet 1
1. (a) Show that if cfw_u, v is an orthonormal set, then cfw_2 + v , 3 6 is an orthogonal but
uu
v
not orthonormal set.
a b
(b) Show that
has real eigenvalues if and only if a b.
MATH 240 Spring 2013 Exam 3 Solutions
There are 5 questions. Answer each on a separate sheet of paper. Use the back side if needed.
On each sheet, put your name, your section leaders name and your section meeting time.
When a question has a short nal answ
Fall 2006 Math 240 Final
Show all work to receive full credit. Good luck!
a~b
awc
a+b+c
0
Problem 1. [15 points] LetV 2 { , a,b,cany real numbers}.
a. V is a subset of R. What is n?
b. Find a set of vectors that spans V.
c. Justify why V is a subspac
MATH 240 FINAL EXAM May 16, 2003
Instructions: Number the answer sheets from 1 to 9. Fill out all the information at the top of
each sheet. Answer problem n on page n, n = 1, - - - ,9. Do not answer one question on more than
one sheet. If you need more s