Class notes

Class notes Linear Algebra

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Course
Linear Algebra

Institution
Drake University

22 Pages of notes Taken in my linear algebra course, contains topics and notes related to Linear Combinations, Solution Sets/Set Builder Notation, Matrix Operations, Row Reduction, Abstract Vectorspace, Linear Closure/Span, Basis, Dimension, Linear Transformations, Eigenvalues/Eigenvectors. Does no...

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Uploaded on December 28, 2023
Number of pages 22
Written in 2023/2024
Type Class notes
Professor(s) Dr. stefanie wang
Contains All classes

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Lincer Combinations of Vanables
Theorem
1 5 Gauss' Method
.
:

C X,6
,
CXcb . . . Xn c = R ↓ liner system can be
changed to another by one

of these operations
A liner equation in neveriables has the form 1) Our equation swapped with another
) One equation
2
multiplied byis a non-zero scaler

2X
,0 Xb ...

62Xn = d 23d = IR 3) An equation is replaced with the sum of itself is
, ,

a sealer multiple of another equation

* lineer system in neveriables has the form : &
inition These operations or called now operations ,

elementaryrow operations ,
or Gaussian Operations
.

a X +9 24 ... +a
nXn = d
, , ,
, , ,

In eachvor of alimestem
2 X 6 az , 2X26 +az nXn =
da the first ona
,
...

c ,, ,
,

&
k ,, X ,
+
9 2
X
<b
...

+ak nXn = dk
, ,

* lineer system is
in echelon form if the /
We say an notuple (S
,,
Sc
,
"Sn) is a solution the in each now is to the right of the leading verable

previous liner system if it solves each equation . in the preceding equation

W

. See
Definition Al"real") matrix Goal
: is a kxn array of
real :
Augmented matrix into

numbers (K rors
,
n columns) echelon form using now

operations . Due in

I matrix be echelon form
agmented in a natur , you can

the do algebraic substitutions
column represents constants in a
line system

and whos first in columns represent the to solve for all

offerent in an n-variable linear system variables
, provided that
there is a solution

example
kshut2)
↳ A : Geekho , man
o e

nod = 10

Sn -d = So

(sidl) It's 1) .
&
...
>
-

,
,

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