Math 2R3 Assignment #1 Solutions
This assignment was due 11:30am Tuesday September 22.
Exercises from the Lecture Notes: #1, #4, #5, #7 and #9.
1. You are
ying your remote controlled drone above your
Math 2R3 Assignment #5 Solutions
This assignment was due 11:30am Tuesday November 10.
Exercises from the Lecture Notes: #30, #32, #35, #36 and #37.
1. Prove Sylvester inequalities for the rank of the
Math 2R3 Assignment #2 Solutions
This assignment was due 11:30am Tuesday October 6.
Exercises from the Lecture Notes: #10, #11, #12, #13 and #14.
1. Let S
R3 consist of three vectors
v1 = (v11 ; v21 ;
MATH 2R03 Linear Algebra II
Term 2 Summer 2009
Assignment 5
Due: Thursday, July 30
Required Problems Let V be a vector space.
1. Let cfw_b1 , . . . , bn be a basis for V . Then for v, w V , we may wr
2R3 Lecture Notes Chapter 4
E. Sawyer
Math & Stats Department
November 11, 2015
E. Sawyer (McMaster University)
Chapter 4
November 11, 2015
1 / 32
The derivative map through the eyes of Euclid
Recall
Lecture Notes in Linear Algebra
Eric T. Sawyer
McMaster University, Hamilton, Ontario
E-mail address: [email protected]
Contents
Preface
Part 1.
v
1
Linear spaces
Chapter 1. Vectors
1. Velocity vecto
Lecture Notes in Linear Algebra
Eric T. Sawyer
McMaster University, Hamilton, Ontario
E-mail address: [email protected]
Contents
Preface
Part 1.
v
1
Linear spaces
Chapter 1. Vectors
1. Velocity vecto
5. LINEAR INDEPENDENCE OF SETS OF VECTORS
Exercise 10. Let S
23
R3 consist of three vectors
v1
=
(v11 ; v21 ; v31 ) ;
v2
=
(v12 ; v22 ; v32 ) ;
v3
=
(v13 ; v23 ; v33 ) :
3
Prove that Span S = R if and
2R3 Lecture Notes Chapter 5
E. Sawyer
Math & Stats Department
November 19, 2015
E. Sawyer (McMaster University)
Chapter 5
November 19, 2015
1 / 49
The dot product
The familiar dot product of two vecto
Lecture Notes in Linear Algebra
Eric T. Sawyer
McMaster University, Hamilton, Ontario
E-mail address: [email protected]
Contents
Preface
Part 1.
v
1
Linear spaces
Chapter 1. Vectors
1. Velocity vecto
2R3 Lecture Notes Chapter 6
E. Sawyer
Math & Stats Department
November 25, 2015
E. Sawyer (McMaster University)
Chapter 6
November 25, 2015
1 / 59
Inner product space isomorphism
Recall that a matrix
Mathematics 2R3 Practice Test 1
Last Name:
Initials:
Student No.:
The test is 50 minutes long.
The test has 7 pages and 5 questions and is printed on BOTH sides of the paper.
Page 7 contains no que
MATHEMATICS 2R03 SAMPLE EXAM
1
SURNAME_Given Name_
Student Number_
MATHEMATICS 2R03
SAMPLE FINAL EXAMINATION
DURATION: 3 HOURS
MCMASTER UNIVERSITY
DR. E. SAWYER
DAY CLASS
DECEMBER 2015
THIS EXAMINATIO
NAME:
STUDENT ID:
MATH 2R03 Linear Algebra II
Term 2 Summer 2009
Test 2
Thursday, July 23
There 5 questions on 10 pages. There are two additional pages for your scratch work.
Some questions have multi
NAME:
STUDENT ID:
MATH 2R03 Linear Algebra II
Term 2 Summer 2009
Test 1
Thursday, July 9
There 6 questions on 10 pages. Some questions have multiple parts. Read each
question carefully and write your
2R03 - Lecture summary
2016/06/21
4.1
Real vector spaces
I Definition 1: vector space
I Examples: zero vector space (Ex. 1), Rn (Ex. 2), R (Ex. 3), matrices Mmn (Ex. 4, 5), real
valued functions on (,
Lecture Notes in Linear Algebra
Eric T. Sawyer
McMaster University, Hamilton, Ontario
E-mail address: [email protected]
Contents
Preface
Part 1.
v
1
Linear spaces
Chapter 1. Vectors
1. Velocity vecto
Math 2R3 Midterm Test Solutions
1. Show that the set S = f(3; 7; 1) ; ( 1; 3; 0) ; (4; 4; 1)g of vectors in R3 is linearly dependent, and express each of them as a linear combination of the other two.
Example (temp.mtw): The data below gives observed maximum temperature readings in
Centigrade over five days in May.
14, 7, 20, 16, 18, all in oC
2
For this data x = 15, mx = 16, s x = 25, and sx = 5
S
The Sample Variance s2 and Sample Standard Deviation s on Minitab
Example (sheets.mtw): A steel mill manufactures metal sheets of nominal thickness .13 cm for
use in industry. A quality control engine
Math 2R3 Assignment #6 Solutions
This assignment was due 10:30am Tuesday December 6.
Exercises from the Lecture Notes: #37, #38, #40, #43 and #47.
Bonus exercises: #48 and #50.
1. Describe in words th
Math 2R3 Assignment #7 Solutions
This assignment was not to be handed in.
Exercises from the Lecture Notes: #51, #54, #55, #56 and #58.
1. Suppose that u; v are two vectors in a real inner product spa
Math 2R3 Assignment #2 Solutions
This assignment was due 11:30am Tuesday October 6.
Exercises from the Lecture Notes: #10, #11, #12, #13 and #14.
1. Let S R3 consist of three vectors
v1 = (v11 , v21 ,
Math 2R3 Assignment #7
Not to be handed in. Solutions will be posted Tuesday December 6.
Exercises from the Lecture Notes: #51, #54, #55, #56 and #58.
1
Math 2R3 Assignment #3 Solutions
This assignment was due 9:30am Thursday October 27.
Exercises from the Lecture Notes: #17, #18 and #19.
1. Show that for any 2 R the set S
basis for R3 .
Consider the
Mathematics 2R3 Test 1
Dr. Bradd Hart g Oct. 3, 2017
\
Last Name: 0 LTR OM/g . Initials:
Student No.:
a The test is 50 minutes long.
0 The test has 6 pages and 5 questions and is printed on BOTH sid