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Class notes & Exercises for linear algebra- 201-NYC

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This document is designed to provide you with comprehensive notes and exercise practice for linear algebra. It offers clear explanations, step-by-step examples, and a variety of exercises to reinforce your understanding. Whether you’re a student looking to improve your skills or a professional seeking to refresh your knowledge, this resource will guide you through the key concepts and applications of linear algebra, making your learning experience both effective and engaging. Dive in and elevate your understanding today!

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Institution
Dawson College ( )
Course
201-NYC

Content preview

,Linear
Algebra Class 1

1) Solving Linear System Using Gaussian &
Gauss-Jordan Elimination
.


· Linear system is made up of linear
equation .




E
3x +
2y = 7
X
4y = 3
-




·
Find variables X BY that satisfy both
equation .


ASIDE : Linear equation is an
equation
of the form :



92Xz + &gXz +
9 , X, + ...




L
Coefficient ↳ variable

·
common example in R
- I dimension

·

Equation of a line >
- ax +
by =
C


·
In R3
↳ 3 dimension

-a constant
ax +
by + c =

, ·
The
following not linear

X+ have power
y3 3
any
&
=




# ,
+ X +
X - 7 =
0 other than 1
linear
not
equation

A Linear system can
only have 3 possible
·




outcome.

1
Unique Solution

3
.




Consistent
.
2 Infinite # of solution

. No
3 solution inconsistent
>
-
system

·

Example in R2 :

①2x
②[
1 5
E
+ =




3X 0
y
-
=




③

, D

- * (1 3)
,




5x =
5
X = 1
3
y
=




②
2(zX + y 5) =


-
4x +
2y = 5



Yfinite
4x
2y 18
-


+ =




e, Be
are the same


* Infinite solutions we use , parameters

with
parametic solutions we usually
isolate the .
first variable
5 line
Grepresent
2X + same
y
=




4x + 10
2y
=
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Institution
Dawson College ( )
Study
Health Science
Course
201-NYC

Document information

Uploaded on
September 20, 2024
Number of pages
107
Written in
2021/2022
Type
Class notes
Professor(s)
Jihane
Contains
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Subjects

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