Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 8 solution
1. Let A be an invertible matrix.
(i) Use mathematical induction to prove t
Nanyang Technological University
Semester II, 2007-2008
H3 Numbers and Matrices
Examination
INSTRUCTIONS TO CANDIDATES
This examination paper contains SIX (6) questions and comprises FIFTEEN (15 )
pr
Nanyang Technological University
Semester II, 2008-2009
H3 Numbers and Matrices
Examination
INSTRUCTIONS TO CANDIDATES
This examination paper contains SIX (6) questions and comprises FIFTEEN (15 )
pr
Nanyang Technological University
Semester II, 2009-2010
H3 Numbers and Matrices
Final exam
INSTRUCTIONS TO CANDIDATES
Time allowed: 120 minutes.
This test paper contains SIX (6) questions and compri
Nanyang Technological University
Semester II, 2007-2008
H3 Numbers and Matrices
Examination
INSTRUCTIONS TO CANDIDATES
This examination paper contains SIX (6) questions and comprises FIFTEEN (15 )
pr
Nanyang Technological University
Semester II, 2010-2011
NTU H3 Numbers and Matrices
Examination
12th May 2011
3.30pm 5.30pm
Name:
Question
1
2
3
4
5
6
Total
Marks
INSTRUCTIONS TO CANDIDATES
This exam
Nanyang Technological University
Semester II, 20062007
H3 maths Numbers and Matrices
Mid term test 1
Date: 14 February 2007
Time allowed: 1 hour.
INSTRUCTIONS TO CANDIDATES
This examination paper con
Nanyang Technological University
Semester II, 2009-2010
H3 Numbers and Matrices
Final exam
INSTRUCTIONS TO CANDIDATES
Time allowed: 120 minutes.
This test paper contains SIX (6) questions and compri
Nanyang Technological University
Semester II, 20062007
H3 Mathematics Numbers and Matrices
Final Examination
Date: 16 May 2007
Time allowed: 2 hours.
INSTRUCTIONS TO CANDIDATES
This examination paper
1
Solutions to Final Exam of 2008
1. Question 1.
(a) (i) The symbol a|b means that there exists some integer c such that b = ac.
(ii) The symbol a b (mod m) means m|(a b), i.e. (a b) is divisible by m
1
Solutions to Final Exam of 2009
1. Question 1.
(a) 8x 6 (mod 10) is equivalent to 4x 3 (mod 5) and 3x 15 (mod 21) is
equivalent to x 5 (mod 7). Thus we are solving the following system of linear
con
Nanyang Technological University
Semester II, 20062007
H3 Mathematics Numbers and Matrices
Final Examination
Date: 16 May 2007
Time allowed: 2 hours.
INSTRUCTIONS TO CANDIDATES
This examination paper
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2008
Revision Problems Test 1
1. Is the following statement true or false?
Let n be a positive integ
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 9
Reading Determinants.
1. The following Hill 2-cipher is intercepted
LAN EQEIL
Given
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 9
Reading Determinants.
1. The following Hill 2-cipher is intercepted
LAN EQEIL
Given
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 10
Reading for this tutorial: Linear Transformations
1. A transformation T refers to a
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 10 solution
1. A transformation T refers to a function from Rn to Rm . Here, the vecto
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 11
1. A country is divided into three demographic regions. It is found that each year
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 11 solution
1. A country is divided into three demographic regions. It is found that e
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 12
1. For each of the following, a set of objects is given together with operations an
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 13 solutions
1. For each of the following, a set of objects is given together with ope
Nanyang Technological University
SPMS/Division of Mathematical Sciences
H3 Numbers and Matrices - 2013
Tutorial 14
Reading for this tutorial: Linear combinations, span, linear independence,
basis, dim
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2013
Tutorial 14 solutions
1. Which of the following sets of vectors in R3 are linearly independent
Nanyang Technological University
SPMS/Division of Mathematical Sciences
NTU H3 Numbers and Matrices 2010
Tutorial 15
1. Consider the bases B = cfw_v1 , v2 , v3 and B = cfw_v1 , v2 , v3 of R3 , where
Nanyang Technological University
Semester II, 2008-2009
H3 Numbers and Matrices
Test 1
INSTRUCTIONS TO CANDIDATES
Time allowed: 60 minutes.
This test paper contains FOUR (4) questions and comprises
Nanyang Technological University
Semester II, 2007-2008
H3 Numbers and Matrices
Mid-Term Test 1
INSTRUCTIONS TO CANDIDATES
This test paper contains FOUR (4) questions and comprises FIVE (5) printed p
Nanyang Technological University
Semester II, 20062007
H3 maths Numbers and Matrices
Mid term test 2
Date: 4 April 2007
Time allowed: 1 hour.
INSTRUCTIONS TO CANDIDATES
This examination paper contain
1
Solutions to Test2 of April 4, 2007
1. Question 1.
(a) A being invertible means that there exists an n n matrix B such that BA =
AB = In , where In is the n n identity matrix. In this case, B is cal
Nanyang Technological University
Semester II, 20062007
H3 maths Numbers and Matrices
Mid term test 1
Date: 14 February 2007
Time allowed: 1 hour.
INSTRUCTIONS TO CANDIDATES
This examination paper con