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04.02.1
Chapter 04.02
Vectors
After reading this chapter, you should be able to:
1.
define
a vector,
2.
add and subtract vectors,
3.
find linear combinations of vectors and their relationship to a set of equations,
4.
explain what it means to have a linearly independent set of vectors, and
5.
find the rank of a set of vectors.
What is a vector?
A vector is a collection of numbers in a definite order.
If it is a collection of
n
numbers, it is
called a
n
dimensional vector.
So the vector
A
given by
=
n
a
a
a
A
2
1
is a
n
dimensional column vector with
n
components,
n
a
a
a
,......
,
,
2
1
.
The above is a
column vector.
A row vector
]
[
B
is of the form
]
,....
,
,
[
2
1
n
b
b
b
B
=
where
B
is a
n

dimensional row vector with
n
components
n
b
b
b
,....
,
,
2
1
.
Example 1
Give an example of a 3dimensional column vector.
Solution
Assume a point in space is given by its
)
,
,
(
z
y
x
coordinates.
Then if the value of
5
,
2
,
3
=
=
=
z
y
x
, the column vector corresponding to the location of the points is
=
5
2
3
z
y
x
.
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