Math461 Midterm 2
Prof. Konstantina Trivisa
March 31, 2016
Instructions: Read each problem carefully. Write clearly and show all your work in your
notebook. You may NOT use calculators.
Problem 1. (30
Name:
Date: 6-27-08
Exam 2
Remember to show all work. No calculators, notes, or books are allowed on this Quiz. When answering
True/False questions write the entire word. No proof is needed. A stateme
Math 461 ~ Spring 2017 Exam 1
Name:
Instructions: Write your name above. There are six questions (on both sides). Answer
each question on a separate answer sheet. Use the back side if necessary. On ea
Math 461 Exam 2 Fall 2017
Instructions: There are 6 questions (on both sides) worth a total of 100 points. Answer
each question on a separate answer sheet. Use the back side if necessary. On each shee
Final Exam
Math 461
Spring 2017
The use of calculators and notes is prohibited. True/False questions require no justification. Write one
problem per answer sheet and label each answer sheet with your
Math 461 Spring 2017 Exam 2
Name:
Instructions: Write your name above. There are six questions (on both sides). Answer
each question on a separate answer sheet. Use the back side if necessary. On each
Math 461 Spring 2017 Exam 2
Name:
Instructions: Write your name above. rIhere are six questions (on both sides). Answer
each question on a separate answer sheet. Use the back side if necessary. On eac
MATLAB Project 2: MATH 461, Fall 2017
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 pr
DEPARTMENT OF MATHEMATICS
Student's Name Sea Tu tame; . CoursesL i Prob.# i Date
GRADING
Section Instructor Sec.#
HONOR PLEDGE: I pledge on my honor that i have not given or received any
unauthorized
Homework 5
Math 461
Due Tuesday, October 21st.
Problem 1 Let A be the matrix
1 4
1
3
0 0
7
7
A=
3 12 18 12 .
2 8 5 1
Find a basis for the column space and null space of A.
Solution: A in row reduce
Homework 3
Math 461
Due Tuesday, September 30th.
Problem 1 Let A be the matrix
4
2
3
A = 16 6 17 .
12 16 10
Complete a LU -decomposition of A. Recall, you nd a sequence of row operations R1 , . . . ,
Homework 1
Math 461
Due Tuesday, September 23rd.
Problem 1 Consider the matrices,
A=
1 2
B = 1 6 .
0 1
1 0 2
1 1 3
Calculate AB. For any vector y = (y1 , y2 )t , nd a vector x R3 such that Ax = y.
Pro
Homework 1
Math 461
Due Tuesday, September 16th.
Problem 1 Consider the matrix
cos sin
sin cos
U=
.
Let v, w be any 2-dimensional vectors. Show that (U v) (U w) = v w. Also, show that
|U v| = |v|
An
Homework 4
Math 461
Due Tuesday, October 14th.
Problem 1 Let A be the matrix
1 4 0
A = 2 8 1 .
5 1 13
Complete a LU -decomposition with partial pivoting of A. That is, nd a lower triangular
L, upper t
Homework 5
Math 461
Due Tuesday, October 21st.
Problem 1 Let A be the matrix
1 4
1
3
0 0
7
7
A=
3 12 18 12 .
2 8 5 1
Find a basis for the column space and null space of A.
Problem 2 Let A be an m n
Math 461 Spring 2017 Exam 1
Name:
Instructions: Write your name above. There are six questions (on both sides). Answer
each question on a separate answer sheet. Use the back side if necessary. On each
Following Justins Guide to MATLAB in MATH 461 - 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
Math 461 Getting started with MATLAB
University of Maryland, College Park Fall 2017
As a student, you can download MATLAB for free on your own computer from TerpWare:
https:/terpware.umd.edu. Be sure
Math 461/Fall 2013/Jerey Adams
Solutions to Homework 5, Due 10/4
Section 2.5 #2, 4, 6, 8, 10
#2. First solve Ly = b, i.e.
1 00
2
x
2 1 0 y = 4
0 11
6
z
2
So x = 2, 2x + y = 4 y = 2x 4 = 0 and y + z
LU Factorization
One-to-one and onto
Rank, dimension, row space, col space, null space
Bases, change of basis
Determinants, Changing area by determinants
Difference equations
Diagonalization
Discrete
Math 461/Fall 2013/Jerey Adams
Review for Exam 2
1. Chapter 2, Sections 2.8 and 2.9
2.8 Subspaces of Rn : denition of subspace, column space, null space,
basis of a subspace
2.9 Dimension and Rank: co
MATH461 - Midterm 2 Solutions
Problem 1
(a) To find a basis for the null space, solve Ax = 0. From the row reduced matrix, this simplifies to
x1 2x2 x4 = 0,
x3 + 2x4 = 0.
Our free variables are x2 and