Paragon International University
Faculty of Mathematics and Science
MATH 241 Linear Algebra
Academic Year 2023-2024
Assignment 1: Vectors
Out: November 2, 2023
Due: November 9, 2023
Submitted by Chilong Chov
Date: 11/7/2023
1. Write a paragraph about your expectations for this course.
As a Civil Engineering student, my expectations for this course is to understand essential
tools that will be beneficial for me in the future. I have read the course syllabus and
acknowledge that upon completion of this course, I will be able to solve linear equations,
systems, and other mathematical problems related to matrix and vector by applying them
into the term project.As I did some research, these topics are essential for understanding
the behavior of structures, analyzing stresses and strains, and designing efficient and safe
structures. More importantly, I definitely expect the lecturer to deliver the knowledge
interestingly and interactively because I do believe that no matter how knowledgeable a
professor is, if the lecture is boring, students won’t get most of the information they need
to know.
2. What is a vector and what are the applications of vectors in your field? Please explain
with examples.
As a sophomore, I haven’t got much experience in the actual field. We mostly learn
basic subjects during our freshman year, but as I did some research recently, this is
what I found:
● Structural Analysis: Vectors are used to represent forces acting on structures, such as
buildings, bridges, and dams. By analyzing the forces acting on a structure, engineers
can design it to withstand the stresses and strains that it will be subjected to.
● Fluid Mechanics: Vectors are used to represent the flow of fluids, such as water and
air. By understanding the flow of fluids, engineers can design hydraulic systems, such
as dams, pumps, and turbines.
● Geotechnical Engineering: Vectors are used to represent stresses and strains in soil
and rock. By understanding the behavior of soil and rock, engineers can design
foundations, slopes, and tunnels.
● Geotechnical Engineering: Vectors are used to represent stresses and strains in soil
and rock. By understanding the behavior of soil and rock, engineers can design
foundations, slopes, and tunnels.
3. Who was Pythagoras, and what was his biggest contribution in Mathematics? Explain
his theorem in detail.
Pythagoras was an Ionian Greek philosopher, mathematician, and scientist from the
island of Samos. He is often regarded as the first pure mathematician and the father
of numbers, and is best known for the Pythagorean theorem.
He made significant contributions to the fields of geometry, music, and astronomy.
Pythagoras' most famous contribution to mathematics is the Pythagorean theorem,
which states that in a right-angled triangle with one 90 degree angle, the square of
the hypotenuse is equal to the sum of the squares of the other two sides.
Equation: a² + b² = c²
↳.
A( 4,3),B(2,0)
-
As
=6,-3)
B
8
.
8
->
AB
⑧
5.d a 2b
+
=
-Is)
C
-
[?] -[?)
-e
[?] [?] -[2]
+
-
[n]
-
d
Thus
6.
Since
[e7
=
I =.r 0
=
[].(a)--
=
2a a 1
+
+
Thus
-
2a 0
a
=
=
-
1
(*)
PrejV=
7.
=
a
[?], =[ ]
4.T
=
3 2 21
+
=
-
+
20
=
4.I g 1 49 59
=
=>
So
=
+
+
Presar=(89). [?]
Pry=(el
e
8.
(U+V) (n=v) 1uK2-HUI2
we
have (UAV), (UV) (ni-vi) +(u2-vg") +...
=
=
(Un+UnY
+
=(4,8 +Ug2+... un2)-(V,+Vet
+
bull-
but
Un2
rnt=ig2+..+
IIUll2=U12 + Ue2+.- Un
->
same
+
as
Thus
V,2+Va+--+ Un2
IVII2=
(U+V). (U-v) IU12- 1IUII"
=
...
Un2
+