MTH 4100, Lecture 3
Systems of n Equations in n Variables, Gaussian Elimination,
Matrix Multiplication, Inverses
E Fink
February 7, 2016
E Fink
MTH 4100, Lecture 3
1/15
1. Systems of n equations in n variables
We can write a system like, say,
2x
6x
4x
+
y
Linear Algebra
Done Wrong
Sergei Treil
Department of Mathematics, Brown University
Copyright c Sergei Treil, 2004, 2009, 2011, 2014
Preface
The title of the book sounds a bit mysterious. Why should anyone read this
book if it presents the subject in a wro
MTH 4100, Lecture 7
Column Space, Null Space, Echelon Form
E Fink
February 23, 2016
E Fink
MTH 4100, Lecture 7
1/15
1. The Column Space
Here comes our rst big example of a subspace.
Denition 68 (Column Space)
The column space of a matrix A (denoted col A)
MTH 4100, Lecture 5
LU Decomposition What, Why, How, and When
E Fink
February 11, 2016
E Fink
MTH 4100, Lecture 5
1/15
1. Inverses and Factoring
Whenever you invert a matrix, you can think of it as factoring that matrix into
a product of elementary matric
MTH 4100, Lecture 6
Transposes, Permutations, Vector Spaces, Subspaces
E Fink
February 21, 2016
E Fink
MTH 4100, Lecture 6
1/15
1. Transposes
Denition 51 (Transpose)
If A is any matrix, the transpose of A, written AT , is the matrix obtained by
exchanging
Answers to exercises
LINEAR ALGEBRA
Jim Hefferon
http:/joshua.smcvt.edu/linearalgebra
Notation
R, R+ , Rn
N, C
(a . b), [a . b]
.
hi,j
V, W, U
v, 0, 0V
Pn , Mnm
[S]
B, D , ,
En = e1 , . . . , en
V=W
MN
h, g
t, s
RepB (v), RepB,D (h)
Znm or Z, Inn or I
|T