The University of New South Wales
School of Mathematics and Statistics
MATH2501 LINEAR ALGEBRA
Session 1, 2016
SAMPLE TEST 2
Students surname
Given name or initials
Student number
Time allowed: 45 minutes.
Question 1
(3 marks)
Write, as usual, X T for the
MATH2501, Linear Algebra
Test 2 Solutions, Semester 1 2016
1. Version A
(1) (3 marks) Write V for the vector space of all polynomials with real coefficients, and define
Z1
< f, g >=
x2 f (x)g(x)dx.
1
Does this give an inner product on V ? If so, prove it;
MATH2501, Linear Algebra
Test 1 Solutions, Semester 1 2016
1. Version A
(1) (8 marks)
Consider the matrix and vectors
1 3 4
A = 3 1 0
1 3 2
1
5 ,
5
11
~y = 1
1
b1
and ~b = b2 .
b3
(a) Find all solutions of A~x = ~y , and write your answer in vector f
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra 1
P.G. Brown
Chapter 10: - The Jordan Form.
In our previous work, we have seen that a square n n matrix A is diagonalisable if A has
a full quota of n linearly independent eigenve
MATH 313 Elementary Linear Algebra
L. Zhao
Contents
Chapter 1. Linear Equations in Linear Algebra
1. Systems of Linear Equations
2. Row Reduction and Echelon Forms
3. Vector Equations
4. The Matrix Equation Ax = b
5. Solutions Sets of Linear Systems
6. Li
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra
P.G. Brown
Chapter 12: - Systems of Dierential Equations.
Having learnt how to compute exponentials of matrices, we will look at the applications of
this to solving systems of die
MATH2501 Linear Algebra, S1 2016
Answers to selected problems
1. LINEAR EQUATIONS AND MATRICES
Note. For linear systems with infinitely many solutions there are many ways of writing the
solutions. If your answers do not match the following they may still
School of Mathematics and Statistics
The University of New South Wales
MATH2501 LINEAR ALGEBRA
Session 1, 2016
TEST 3
VERSION 1
This sheet must be filled in and stapled to the front of your answers
Students Surname
First name or Initials
Tutorial Code
Stu
MATH2501, Linear Algebra
Test 1 Solutions, Semester 1 2017
1. Version A
(1) (8 marks)
Consider the matrix and vectors
1 2 1
A = 2 1 3
1 7 6
1
1 ,
2
4
~y = 6
6
b1
and ~b = b2 .
b3
(a) Find all solutions of A~x = ~y , and write your answer in vector for
FACULTY OF SCIENCE
SCHOOL OF MATHEMATICS AND
STATISTICS
MATH2501 LINEAR ALGEBRA
Semester 1, 2017
Cricos Provider Code 00098G
c School of Mathematics and Statistics UNSW 2014
MATH2501 Course Outline
Information about the course
Course authority. P.G. Brown
MATH2501 Linear Algebra, S1 2016: Problems
1. LINEAR EQUATIONS AND MATRICES
1. For each of the following matrices A and vectors b, use Gaussian elimination to find the general
solution of the system Ax = b.
1 4 1
12
2 , b = 7;
a) A = 1 3
2 9 2
35
0 3
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
JUNE 2015
MATH2501
Linear Algebra
(1) TIME ALLOWED THREE HOURS.
(2) TOTAL NUMBER OF QUESTIONS 5
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF EQUAL VALUE
(5) THIS PAPER MAY BE RETA
University of New South Wales
School of Mathematics
MATH2501 LINEAR ALGEBRA
Session 1, 2006
There are two lecturers for this subject.
David Angell (weeks 17)
Red Centre 3093
[email protected]
phone 9385 7061
David Crocker (weeks 814)
Red Centre 309
University of New South Wales School of Mathematics
MATH2501 Linear Algebra
Problems, notes and questions
Example. Let
1. LINEAR EQUATIONS AND MATRICES
Systems of linear equations.
Objectives. To be able to determine how many solutions a system of
linear
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra 1
P.G. Brown
Chapter 8: - Symmetric Matrices.
Conics in R2 :
Sketch the curve 5x2 + 4xy + 8y 2 = 36.
We can plot this on MAPLE using the implicitplot command.
At least three obvio
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra 1
P.G. Brown
Chapter 11: - Functions of Matrices.
Exponential of a matrix. We turn to the problem of giving a meaning to etA and
similar expressions, where A is a square matrix.
W
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra 1
P.G. Brown
Chapter 9: - The Cayley Hamilton Theorem.
Consider the 2 2 matrix
(
A=
2 1
3 1
)
.
Show that A2 = A + 5I and hence find A4 .
The above example invites a range of ques
UNSW AUSTRALIA
SCHOOL OF MATHEMATICS AND STATISTICS
MATH2501 Linear Algebra 1
P.G. Brown
Chapter 7: - Orthogonal Transformations.
In this chapter we are going to consider linear transformations in 2 and 3 dimensions that
preserve lengths. One such transfo
The University of New South Wales
School of Mathematics and Statistics
MATH2501 LINEAR ALGEBRA
TEST 1
Students surname
Session 2, 2012
Version A
Given name or initials
Student number
Hint. By reading through the whole of each question before you start, yo
THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND STATISTICS
JUNE 2014
MATH2501
Linear Algebra
(1) TIME ALLOWED THREE HOURS.
(2) TOTAL NUMBER OF QUESTIONS 5
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF EQUAL VALUE
(5) THIS PAPER MAY BE RETA
The University of New South Wales
School of Mathematics and Statistics
MATH2501 LINEAR ALGEBRA
SAMPLE TEST 3
Students surname
Given name or initials
Student number
Time allowed: 40 minutes.
Question 1
(4 marks)
Let
6 2
A= 2 9
1 2
3
6
2
1
and v = 2 .
1
(a
FACULTY OF SCIENCE
SCHOOL OF MATHEMATICS AND
STATISTICS
MATH2501
LINEAR ALGEBRA
Session 2, 2007
MATH2501 Course Outline
Information about the course
Course Authority:
Dr. T. Bates
Lecturer: Dr. T. Bates RC-6107, email [email protected]
Consultation: Times will