MA1101R: Answers/Solutions of Exercise 1
(Version: January 29, 2011)
1. (a), (c), (f) are linear equations. (b), (d), (e) are not.
2. (a) is a linear equation. (b) is a linear equation if k = 0. (c) i
MA1100 Homework Set 5 (with solutions)
Semester 1, 2011/2012
Problems
Relations
1. Let A = cfw_a, b, c. Consider the following relations on A. Determine whether
each relation is reexive, symmetric or
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 10 (31/1004/11)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected q
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 4 (12/0916/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 3 (05/0909/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 4
Semester I 2010/11
MA1101R Laboratory 4
Matrix Operations, Eigenvalues and Diagonalization
In this laboratory session, w
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 2 (29/0802/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 3
Semester I 2010/11
Transformation Matrices
In this laboratory session, we will use the specially written matlab function
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 1 (22/0826/08)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 2
Semester I 2010/11
Solving Systems Of Linear Equations
In this laboratory session, we continue to explore working with s
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
MA1102R Calculus
Solution to Tutorial 11
Tutorial Part I (Partial)
1
dy
dy
1. (a) Suppose 2 xy
= 1, x, y > 0. Then y
= . Integrate with respect
NATIONAL UNIVERSITY OF SINGAPORE
Department of Mathematics
MA1101R Laboratory 1
Semester I 2010/11
A Very Brief Introduction to MATLAB
and Matrix Operations
In this laboratory session, we introduce so
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
MA1102R Calculus
Solution to Tutorial 10
Tutorial Part I (Partial)
1. Solving x4 = 8x, we have x = 0 and x = 2. Note that 8x x4 on [0, 2]. Then t
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 5 (26/0930/09)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
HW4:CommonMistakes/problems/GeneralComments
Q1(d) Some students did not use arrows (in arrow diagrams) but merely straight links to link the
elements in the domain and the co-domain, giving rise to am
MA1100 Homework Set 2
Semester 1, 2011/2012
Please read:
Do all the problems below and submit on September 16 (Friday) during lecture.
Use A4 size paper. Write your full name, student number and tut
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 9 (24/1028/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
MA1100 Homework Set 2 Hints
1. Use direct proof for (a) and contrapositive proof for (b). For (c), you should
apply (a) and (b) without having to rewrite their proofs again.
2. Use direct proof and de
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 8 (17/1021/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
MA1100 Homework Set 1
Semester 1, 2011/2012
Please read:
This is NOT the same as your tutorial set.
Do all the problems below and submit on September 2 (Friday) during lecture.
Use A4 size paper. W
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 7 (10/1014/10)
MA1102R Calculus
Tutorial Part I
This part will be discussed during the tutorial session. Partial solution of selected qu
MA1100 Homework Set 1 Hints
1 There are many possible answers:
(a) Refer to Chartrands exercise Qn 1.7.
(b) One possibility is to use power set of S as the underlying set, and cardinality
in the under
NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2011/2012
Tutorial 6 (03/1007/10)
MA1102R Calculus
Tutorial Part I
This tutorial will be discussed during the e-learning week. The complete solution will b