MATH 1104 ABCDE Final/Deferred Exam
April 2006
Page
2
1 2
1
2 5 3
1. Let A = 1 3 and let B =
.
4 2 1
6
4 2
What is the second column of AB.
2. If A
a)
1 2
1 4
8
b) 2
4
7
a) 2
22
6
6
2 1
=
2
c) 8
4
d)
13
8
2
21
2
e) 8
4
2 4
, what is A?
2 2
b)
BIT 1101A
Answers to Test 3
Instructor: Dr. A. Alaca
1. U =
Span
November 6, 2006
1
1
1
1 , 0 and W = Span 0 .
0
1
1
Thus U and W are subspaces.
V and H do not have the zero vector, so they are not subspaces.
Answer is d.
3a
3b
3c
2. det u 2x v
MATH 1104B, Practice Problems
MATH 1104B Linear Algebra
for Engineering and Computer Science Students
Practice Problems for Winter 2006
Instructor:
Dr. Ayse Alaca,
Herzberg Physics Office #4348
Tel: (613) 520 2600 Ext. 2133
Electronic mail: [email protected]
MATHEMATICAL TRIPOS
Monday 2 June 2003
Part II
Alternative A
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
Each question is divided into Part (i) and Part (ii), which may or may not be
related. Candidates may attempt either or b
MATHEMATICAL TRIPOS
Tuesday 6th June, 2006
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question
MATHEMATICAL TRIPOS
Wednesday 8 June 2005
Part IB
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four que
MATHEMATICAL TRIPOS
Monday 31 May 2004
Part II
Alternative B
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
The number of marks for each question is the same.
Additional credit will be given for a substantially complete answer.
W
MATHEMATICAL TRIPOS
Friday 4 June 2004
Part IB
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Sect
MATHEMATICAL TRIPOS
Friday 9th June, 2006
Part IB
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four que
MATHEMATICAL TRIPOS
Thursday 29 May 2003
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I. In
Section I, you may attempt all four questions. In S
MATHEMATICAL TRIPOS
Monday 6 June 2005
Part IA
9 to 12
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sectio
MATHEMATICAL TRIPOS
Tuesday 1st June 2004
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four
MATHEMATICAL TRIPOS
Friday 2nd June, 2006
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question i
MATHEMATICAL TRIPOS
Friday 28th May 2004
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four q
MATHEMATICAL TRIPOS
Wednesday 2 June 2004
Part IB
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from S
MATHEMATICAL TRIPOS
Thursday 9 June 2005
Part II
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in
MATHEMATICAL TRIPOS
Monday 5th June, 2006
Part IA
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question i
MATHEMATICAL TRIPOS
Thursday 1st June, 2006
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in S
MATHEMATICAL TRIPOS
Wednesday 2 June 2004
Part II
Alternative A
9 to 12
PAPER 2
Before you begin read these instructions carefully.
Each question is divided into Part (i) and Part (ii), which may or may not be
related. Candidates may attempt either or bot
MATHEMATICAL TRIPOS
Tuesday 7 June 2005
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in
MATHEMATICAL TRIPOS
Thursday 9 June 2005
Part IB
9 to 12
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four questions
MATHEMATICAL TRIPOS
Thursday 5 June 2003
Part IB
9 to 12
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Section
MATHEMATICAL TRIPOS
Thursday 2 June 2005
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sect
MATHEMATICAL TRIPOS
Friday 30 May 2003
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I. In
Section I, you may attempt all four questions. I
MATHEMATICAL TRIPOS
Tuesday 1 June 2004
Part IB
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Section
MATHEMATICAL TRIPOS
Monday 6 June 2005
Part II
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in S
MATHEMATICAL TRIPOS
Friday 9 June 2006
Part II
9 to 12
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sectio
MATHEMATICAL TRIPOS
Thursday 27th May 2004
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four ques
MATHEMATICAL TRIPOS
Tuesday 6th June, 2006
Part IB
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four questio
MATHEMATICAL TRIPOS
Monday 31st May 2004
Part IA
9 to 12
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four questi