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04.01.1
Chapter 04.01
Introduction
After reading this chapter, you should be able to
1.
define what a matrix is
.
2.
identify special types of matrices, and
3.
identify when two matrices are equal.
What does a matrix look like?
Matrices are everywhere.
If you have used a spreadsheet such as Excel or Lotus or written a
table, you have used a matrix.
Matrices make presentation of numbers clearer and make
calculations easier to program. Look at the matrix below about the sale of tires in a
Blowoutr’us store – given by quarter and make of tires.
Q1
Q2
Q3
Q4
Copper
Michigan
Tirestone
6
5
25
16
10
20
7
15
3
27
25
2
If one wants to know how many
Copper
tires were sold in
Quarter 4
, we go along the row
Copper
and column
Q4
and find that it is 27.
So what is a matrix?
A
matrix
is a rectangular array of elements.
The elements can be symbolic expressions or
numbers.
Matrix
]
[
A
is denoted by
mn
m
m
n
n
a
a
a
a
a
a
a
a
a
A
.......
.......
.......
]
[
2
1
2
22
21
1
12
11
Row
i
of
]
[
A
has
n
elements and is
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View Full Document04.01.2
Chapter 04.01
in
i
i
a
a
a
....
2
1
and column
j
of
]
[
A
has
m
elements and is
mj
j
j
a
a
a
2
1
Each matrix has rows and columns and this defines the size of the matrix.
If a matrix
]
[
A
has
m
rows and
n
columns, the size of the matrix is denoted by
n
m
.
The matrix
]
[
A
may
also be denoted by
n
m
A
]
[
to show that
]
[
A
is a matrix with
m
rows and
n
columns.
Each entry in the matrix is called the entry or element of the matrix and is denoted by
ij
a
where
i
is the row number and
j
is the column number of the element.
The matrix for the tire sales example could be denoted by the matrix [
A
] as
27
7
16
6
25
15
10
5
2
3
20
25
]
[
A
.
There are 3 rows and 4 columns, so the size of the matrix is
4
3
.
In the above
]
[
A
matrix,
27
34
a
.
What are the special types of matrices?
Vector: A vector is a matrix that has only one row or one column.
There are two types of
vectors – row vectors and column vectors.
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 Spring '08
 Kaw,A

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