MATH1107DE Test 1
24 September 2012
Page
1
This test paper has 4 questions and total of 20 marks. It can not be taken from
the examination room. Calculators are allowed. SHOW ALL YOUR WORK. Duration: 50 minutes.
NAME:
STUDENT NUMBER:
1. [5 Marks]Let w = 1

Tutorial 3 solutions
MATH1107 Linear Algebra I
October 1 Fall 2012
(1) We give the inverses of elementary row operations.
To reverse the operation of swapping rows i and j : Ri Rj , perform Ri Rj again.
To reverse the operation cRi , c = 0, multiply the

Homework 3
MATH1107 Linear Algebra I
Fall 2012 Due October 22 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. For this assignement you may assume that we are working over the eld R.

Tutorial 4
MATH1107 Linear Algebra I
Fall 2012 22 October 2012
Be sure to ask your TA with any other questions you may have.
(1) (a) What is the set of vectors in R3 that are orthogonal to
3
4 .
5
3
x
The set of vectors orthogonal to 4 are the vectors y s

Homework 2
MATH1107 Linear Algebra I
Fall 2012 Due on 10 October 2012
(1) All of the given systems of linear equations are over R. For each one, put the system into augmented
matrix form, put the augmented matrix in reduced row-echelon form and use this t

Bonus Questions, Part I
MATH1107 Linear Algebra I
Fall 2012 Due 3 December 2012
Please clearly write your rst name, last name, student number, tutorial section and TAs name on
your assignment and staple the sheets together.
(1) What buttons do you press t

Tutorial 7
MATH1107 Linear Algebra I
Fall 2012 26 November 2012
Be sure to ask your TA any other questions you may have.
(1) Let
23
32
A=
(a) Write out the characteristic polynomial of A and nd its roots.
The characteristic polynomial of A is
pA () = det

MATH1107DE Test 4
19 November 2012
Page
1
This test paper has 4 questions and total of 20 marks. It can not be taken from
the examination room. Calculators are allowed. SHOW ALL YOUR WORK. Duration: 50 minutes.
NAME:
STUDENT NUMBER:
SECTION and TUTORIAL:

MATH1107DE Test 3
29 October 2012
Page
1
This test paper has 4 questions and total of 20 marks. It can not be taken from
the examination room. Calculators are allowed. SHOW ALL YOUR WORK. Duration: 50 minutes.
NAME:
STUDENT NUMBER:
SECTION and TUTORIAL:
T

Tutorial 5
MATH1107 Linear Algebra I
Fall 2012 05 November 2012
Be sure to ask your TA any other questions you may have.
(1) Finding a basis.
(a) Remember from class that you can nd a basis from a spanning set simply by, one-by-one,
removing a vector that

Tutorial 6
MATH1107 Linear Algebra I
Fall 2012 12 November 2012
Be sure to ask your TA any other questions you may have.
(1) For each of the following row operations write out the corresponding 3 3 elementary matrices
and verify that they work as advertis

Tutorial 1
MATH1107 Linear Algebra I
Fall 2012 17 September 2012
(1) Choose two complex numbers, w, z and compute the following:
w+z
w z and z w
wz
w/z and z/w
|w| and |z |
w2 and z 3
Answer: Suppose I picked w = 2 + 3i and z = 1 i. Then I get
w + z

Homework 5
MATH1107 Linear Algebra I
Fall 2012 Due 19 November 2012
Please clearly write your rst name, last name, student number, tutorial section and TAs name on
your assignment and staple the sheets together. For this assignment you may assume that we

Bonus Questions, Part II
MATH1107 Linear Algebra I
Fall 2012 Due December 3 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. Show all your work.
(1) This question is by popular reques

Homework 3
MATH1107 Linear Algebra I
Fall 2012 Due October 22 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. For this assignment you may assume that we are working over the eld R.
(

Homework 5
MATH1107 Linear Algebra I
Fall 2012 Due 19 November 2012
Please clearly write your rst name, last name, student number, tutorial section and TAs name on
your assignment and staple the sheets together. For this assignment you may assume that we

Homework 4
MATH1107 Linear Algebra I
Fall 2012 Due 5 November 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. For this assignment you may assume that we are working over the eld R.
(

Bonus Questions, Part I
MATH1107 Linear Algebra I
Fall 2012 Due 3 December 2012
Please clearly write your rst name, last name, student number, tutorial section and TAs name on
your assignment and staple the sheets together.
(1) What buttons do you press t

Homework 4
MATH1107 Linear Algebra I
Fall 2012 Due 5 November 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. For this assignment you may assume that we are working over the eld R.
(

Bonus Questions, Part II
MATH1107 Linear Algebra I
Fall 2012 Due December 3 2012
Please clearly write your rst name, last name and student number on your assignment and staple
the sheets together. Show all your work.
(1) This question is by popular reques