Vector Calculations 125

Vector Calculations

Even though vectors

have a few special

interpretations, they're a

just

1×n and n×1 matrices...

And they're

calculated in the

exact same way.

= (3 · 1 + 1 · 2) = 5

• (10, 10) + (−3, −6) = (10 + (−3), 10 + (−6)) = (7, 4)

• (10, 10) − (3, 6) = (10 − 3, 10 − 6) = (7, 4)

• 2(3, 1) = (2 · 3, 2 · 1) = (6, 2)

•

•

•

•

•

(3, 1)

•

Aition

10

10

7

4

−3

−6

+

10 + (−3)

10 + (−6)

= =

Subtraction

10

10

7

4

3

6

−

10 − 3

10 − 6

= =

Scalar multiplication

6

2

3

1

2

2 · 3

2 · 1

= =

Matrix Multiplication

3

1

6

2

3

1

1

2

3 · 1 3 · 2

1 · 1 1 · 2

(1, 2) = =

8

2

−3

1

3

1

3

1

=

21

7

8 · 3 + (−3) · 1

2 · 3 + 1 · 1

= = 7

Simple!

126 Chapter 5 Introduction to Vectors

Horizontal

vectors like this

one are caed

row vectors.

And vertical

vectors are

caed column

vectors.

Makes

sense.

We also ca the set of

a n×1 matrices R

n

.

Sure,

why not...

R

n

aears a

lot in linear

algebra, so

make sure you

remember it.

No

problem.

When writing vectors by hand, we

usuay draw the leftmost line

double, like this.

A 2×1

vectors

A

3×1

vectors

A

n×1

vectors

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