NATIONAL UNIVERSITY OF SINGAPORE
SEMESTER 1, 2015/2016
MA1101R Linear Algebra
Homework Assignment 1
Please write your name, matriculation card number and tutorial group number
on the answer script, and submit during either Group 1s lecture on 14th Septemb

Reminder
1. Lab quiz this week.
2. Lab quiz duration: 50 minutes
3. Please bring along your student (matriculation)
card.
4. You are allowed to bring your own rough paper
for working.
5. Open everything quiz.
6. Please arrive at least 5 minutes before the

Mid Term Test Details
Date: 6th March (Thursday)
Time: 4.15pm 5.15pm
Venue: MPSH2 (Sections A&B)
Seating plan (to be uploaded later)
Scope: From beginning to End of Section 3.3
One Helpsheet (A4, double sided, hand written)
Unavailability during recess we

MA1101R
Linear Algebra I
Introductory Lecture (Lecture 00)
S
Welcome
S All NUS students
S All H3 students
S All non-NUS (exchange, NUS High) students
Outline of todays lecture
S Part I: Module information
S Part II: About Linear Algebra
S Part III: Study

Lecture 18 recap
1) Definition of length of a vector, distance, angle, dot product
between two vectors.
2) Dot product and matrix product.
3) Some results on dot products.
4) An example on information retrieval.
5) Orthogonality (orthonormality). Orthogon

Additional information
for H3 students
S
Pre-Registration Process
S Requires the following:
S H3 online Application ID number starting with A (e.g.
A11002067) 1 alphabet, 9 numerical digits.
S 8-character password entered in online NG application
form.
S

This helpsheet is for H3 students only.
All other students need to prepare their
own hand-written helpsheets.
MA1101R Linear Algebra I
Mid-Term Test
Helpsheet for H3 students
Let A = (aij ) be an n p matrix and B = (bij ) be a p m matrix. Then the
(i, j)

Lecture 11 recap
1) Another way to look at linear independence.
2) A theorem on guaranteed dependence.
3) Geometrical interpretation of linear (in)dependence.
4) Adding vectors to a set, preserving independence.
5) Definition of a basis.
6) Uniqueness in

Department of Mathematics, National University of Singapore
2012 / 2013 (Sem 1) MA3236 Nonlinear Programming
Test. Total marks: 100
Time allowed: 90 minutes.
1. [15 points]
Let S be a nonempty closed subset (not necessarily bounded) of R.
(a) Suppose f :

MA3236 NONLINEAR PROGRAMMING
Semester 1, 2014/2015
Mid-term Test
Problem 1 [10 marks]
Consider the function f : R2 R, defined by
f (x) = (x1 x2 )2 + (x1 + 2x2 + 1)2 6x1 x2 .
Is f coercive? Please justify your answer.
Solution.
f (x) = 2x21 + 5x22 4x1 x2 +

MA3236 NONLINEAR PROGRAMMING
Semester 1, 2014/2015
Mid-term Test
Problem 1 [10 marks]
Consider the function f : R2 R, defined by
f (x) = (x1 x2 )2 + (x1 + 2x2 + 1)2 6x1 x2 .
Is f coercive? Please justify your answer.
Problem 2 [15 marks]
Suppose D is a cl

Department of Mathematics, National University of Singapore
2012/2013 (Sem 1)
MA3236 Nonlinear Programming
Tutorial 6a
This is the test for AY 2010/2011 (Sem 1)
Test. Time allowed: 90 minutes
Total marks: 100
1. [30 points]
Consider the function f : R2 R

Definition of matrices, entries, size of a matrix.
Special types of matrices.
Matrix operations and some laws.
Matrix multiplication and differences with real
number multiplication.
Different ways to represent matrix multiplication.
Representing a linear