MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 1
School of Mathematical Sciences, Monash University
These problems cover the work from Week 1, and will be discu
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 2
School of Mathematical Sciences, Monash University
These problems cover the work from Week 2, and will be discu
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 3
School of Mathematical Sciences, Monash University
These problems cover the work from Week 3, and will be discu
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 2
School of Mathematical Sciences, Monash University
These problems cover the work from Week 2, and will be discu
1.9 Application: Economics (A&R 1.9)
Consider an economy consisting of n industries (producing e.g.
commodities such as coal, steel, automobiles, etc), together with
one non-producing sector (e. g. th
MTH2025 Linear Algebra (Advanced)
Quiz 1
School of Mathematical Sciences, Monash University
This is quiz is worth 2% of your total mark for this course. You have 15 minutes to complete the quiz. Write
MTH2021 Linear Algebra with Applications
Quiz 1b
School of Mathematical Sciences, Monash University
This quiz is worth 2% of your total mark for this course. There are 4 questions and you have 15 minu
Theorem 2.2.8. If A is an n X n matrix and E is an n X n elementary
matrix then det(EA) = det(E) det(A).
Tm oiQME/W: %o(d(/\) j 77x (-311
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MTH2021 Linear Algebra with Applications
Quiz 1a
School of Mathematical Sciences, Monash University
This quiz is worth 2% of your total mark for this course. There are 4 questions and you have 15 minu
Once an LU decomposition is known for a coefcient matrix A,
solving a linear system Ax = b can be achieved by performing
substitution twice:
(i) Solve Ly = b for y using forward substitution
(ii) Solv
Denition 4.3.7. A vector space is said to be nite dimensional if
it can be spanned by nitely many vectors.
Theorem 4.3.8. Let V be a nite dimensional vector space and let
B 2 cfw_V1, V2, . . . ,Vn be
Denition 3.3.3. Let A be an m x n matrix. The transformation
TA : R > Rm dened by TA(X) = Ax for all X E R" is a
matrix transformation. We call A the standard matrix for the
transformation TA.
Theorem
E.g. 1.5.10. For each of the following matrices nd its inverse or
show that it is singular:
113 124
020, (b) 3:310.
144 558
3O Theorem 1.5.11. If a square matrix A has either a left inverse B
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 1
School of Mathematical Sciences, Monash University
These problems cover the work from Week 1, and will be discu
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Assignment 1
School of Mathematical Sciences, Monash University
This assignment is worth 5% of your total mark for this cours
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 2
School of Mathematical Sciences, Monash University
These problems cover the work from Week 2, and will be discu
MONASH UNIVERSITY SCHOOL OF MATHEMATICAL SCIENCES
2006
MTHZOIO MULTIVARIABLE CALCULUS
ASSIGNMENT 1 - 2009 [1]
Due: Wednesday 8.4.2009, 5pm
(Please return to your tutor s assignment box
in the 3' oor,
How to Write Mathematics
c Kevin Houston
University of Leeds
September 22, 2009
CHAPTER
0
Preface
Question: How many months have 28 days?
Mathematicians answer: All of them.
The concept
This booklet i
School of Mathematical Sciences
MTH2010 Multivariable Calculus
2017 [1]
Assignment 1
Handed out in support class the week of 13 March
To be submitted in support class the week of 27 March
The complete
Denition W.1.4.7. Let G and H be groups. A function h : G > H
is a homomorphism if h(o - 7') = h(o) - h(T) for all 0,7 E G.
A bijective homomorphism is an isomorphism. Two groups are
isomorphic if the
Proof of Theorem W.2.] .1 .
30 W WA 7% Maa/W (z
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x); 2: saw aw/.
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Z+L Z < 64> (1%
i S P .
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w Wt! D
H
: g
3% 66:4 3W) 54: Wale
W.1 Permutations
W.1.1 Functions
A function f :2 > C from a set D to a set C is a rule that assigns
to each x E D a unique element f (3:) E C. The set D is the
domain, the set C is the codomain, and f
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 1
School of Mathematical Sciences, Monash University
These problems cover the work from Week 1, and will be discu
:(u (2
Mmoloiow W 714/? K(?'
EEOQW W Com 0<\:,30<,
@g/x LLLQ/le cfw_50 $4 (4 ~ (00
g mag imam: (of<
71 MW Was Q3 (MOLUQ/wi
Corollary W. 1. 6. 4. Every 0 E St; can be written as a composition
0 w adjac
MTH2021 Linear Algebra with Applications
MTH2025 Linear Algebra (Advanced)
Problem Set 3
School of Mathematical Sciences, Monash University
These problems cover the work from Week 3, and will be discu
Theorem 4.2.7. A set S with two or more vectors is
(a) Linearly independent ijj no vector in S is expressible as a
linear combination of the other vectors in S.
(b Linearly dependent i at least one of
4 Vector spaces
4.1 Vector spaces and subspaces (A&R 4.1, 4.2)
Denition 4.1.1 (Vector Space). LetWt equipped
with two operations named addition and scalar multi lication.
Addition is a rule that assig
1 Linear systems and matrices
1.1 Systems of linear equations (A&R 1.1)
The original motivation for studying linear algebra was to solve
systems of simultaneous linear equations. E. g.
2x+y+z=5
4m+y+3