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Class notes & Exercises for linear algebra- 201-NYC

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Course
201-NYC

Institution
Dawson College ( )

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 se...

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