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The Manga Guide to Linear Algebra by Ltd. Trend-Pro Co., Iroha Inoue, Shin Takahashi

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What Are Vectors? 121
We, at least we
a made it in!
Try to remember
the minigolf
example while
wetalk about the
next few subjects.
Vectors can be
interpreted in four
dierent ways. Let
me give you a quick
walk-through of a
of them.
7
4
I' use the
1×2
matrix
(7, 4)
and the
2×1
matrix
to make things
simpler.
Okay.
n matrices and n×1 matrices
122 Chapter 5 Introduction to Vectors
The point (7, 4)
x
2
4
7
x
1
O
x
2
4
7
x
1
O
x
2
4
3
743
x
1
O
x
2
4
1
10
107
x
1
O
Interpretation 1
Interpretation 2
Interpretation 3
interpreted as a point in space.
7
4
(7, 4) and are sometimes
In other cases, (7, 4) and
7
4
are interpreted as the
“aow” from the origin
to the point
(7, 4).
(7, 4) and
7
4
can mean the
sum of several
aows equal
to
(7, 4).
And in yet
other cases,
What Are Vectors? 123
x
2
4
7
x
1
O
Interpretation 4
7
4
Finay, (7, 4) and can also
be interpreted as any of
the aows on my left, or
a of them at the same time!
Hang on a second.
I was with you until
that last one...
7
4
How could a
of them be
representations of
(7, 4)
and
when they start
in completely
dierent
places?
While they do start
in dierent places,
they're a the same in
that they go “sevento
the right and four up,”
right?
Yeah, I gue
that's true!
124 Chapter 5 Introduction to Vectors
Vectors are
kind of a
mysterious
concept, don't
you think?
We, they may
sm that way
atfirst.
but...
Once you've got the
basics down, you' be
able to aly them to
a sorts of interesting
problems.
For example,
they're frequently
used in physics to
describe dierent
types of forces.
Cl!
Puing force
Gravitational force

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