Schedule of Instructions MAT 3004 – Applied Linear Algebra
MAT 3004– Applied Linear
Algebra
Prerequisite: Applications of Diffference and Differential Equations
( MAT2002)
Topics
Lecture No.
Module
I
:
Linear
Equations and Matrices
1 Row transformations - Gaussian – elimination & Problems
2 Gauss-Jordan – elimination & Problems
3
Ele
m
entary
m
atrices
–
introduction
4 Lemma 1.7, Theorems 1.8 with proofs, Theorem 1.9, Cor.1.10 stmt only
5 Finding inverse of matrices - Permutation matrix
6
LU factorization and solving s
ystem
of linear equations
L
U factor
ization
–
Problems
Module II: Vector Spaces
7 The Euclidean space
n
R
and Vector spaces – Definition, Examples, Theorem 3.1
with proof
,
theorem 3.2 stmt only
8
Subspace –def, examples, theorem 3.3 statement only, theorem
3.4 with proof
9 Linear combination – Span – examples - theorem 3.5
stmt only
e
s
10
Linearly dependent-independent- bases – (only statements of theorems 3.6, lemma 3.7), theorem 3.8
with proof
11
Dimensions-finite dimensional vector space, Lemma 3.9, Theorems 3.10, 3.11,3.12 only statements,
Corollary 3.13 with proof
12 Construction of bases – examples
Module
III
:
Subspace Properties
13 Row and column spaces – definition-examples, theorem 3.14 only statement
14 Bases for Row and column spaces – examples
15 Rank and nullity – definition, theorem 3.15, stmt only, theorem 3.17, corollary 3.18
with proofs
,
theorem 3.21 stmt only
16
Bases for subspaces, theorem 3.22
–
proof
should be explained as the proof gives the method to
find basis for sum and intersection of subspaces
17 Theorem 3.23
with proof
, Bases for subspaces –Examples
18
Invertibility –theorem 3.24, 3.25, 3.26 only statements , Application to interpolation
Module
I
V:
Linear
Transformations
19 Linear transformation- definition- simple examples
Theorems 4.1, 4.2
with proofs
20
Theorem
4.
3,
Cor. 4.4 statement only;
Linear transformation- examples
21
Inve
rtible
linear transfor
m
ation
, lemma 4.6
with proof
2
2
Theorem 4.7, corollary 4.8
with proofs
23 Matrices of Linear transformations-examples Theorem 4.9 without proof
