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How can matrices help organize information
and how do I manipulate them?
MATRIX: A rectangular
arrangement of
numbers in rows and
columns.
The ORDER of a matrix
is the number of the
rows and columns.
The ENTRIES are the
numbers in the matrix.
This order of this matrix
is a 2 x 3.
columns
rows
 5 9  3
 13  5 0 


8
0

 10
1 3 
0
2 
4  3
 2
1

 7
0
1
3
1
0

9
5 7
1x4
4
6
5 9
2
7
 1

2
(or square
matrix)
3x3
2x2
3
8
6




3x5
(or square
matrix)
0
(Also called a
column matrix)
  9
7
 
0
 
6
4x1
(Also called a
row matrix)
To add two matrices, they must have the same
order. To add, you simply add corresponding
entries.
 5
 3

 0
 3  2
4    3
7   4
1 
0 
 3
5  (2)  3  1 


  33
40 
 0  4
7  (3)
 3
  0
 4
 2
4 
4 
 8 0 1 3   1 7
 5 4 2 9    5 3

 
=
=


5 2

3  2
8  (1)
07
 1 5
3 2
 5 5
43
23
9  ( 2)
7
0
7
7
4
5
5
7


Have you mastered the objective of adding
matrices…go to next slide
If not go to:
http://www.phschool.com
for more practice.
APPLICATION:
Use the data in the tables to answer the following questions.
SATURDAY SCHEDULE
SHIFT
$6.25
$6.50
$7.00
$7.50
DAY
8
3
5
1
EVENING
10
2
2
1
NIGHT
4
1
0
1
SUNDAY SCHEDULE
SHIFT $6.2 $6.50 $7.00 $7.50
5
DAY
5
2
1
1
EVENI
NG
NIGHT
8
2
0
1
2
1
0
1
A. Write the data in each table as a matrix.
B. Add the matrices to find the total number of
workers in each pay category for each work shift.
C. How many weekend employees on the evening
shift earn $6.50?
D. How many weekend employees work the night
shift?
E. Suppose all employees work 8 hour shifts both
Saturday and Sunday. How would you use the
matrix to find the total wages of the weekend
employees?
F. Find the total wages of the weekend employees.
Need some extra help?
Do not get
FRUSTRATED
Go to http://www.phschool.com/
Web code: ate-0201
To subtract two matrices, they must have the same
order. You simply subtract corresponding entries.
 9 2 4   4 0 7   9 4
 5 0 6    1 5  4 

 
   5 1
 1 3 8   2 3 2  1  (2)

 5

 4
 3
20 47 

0  5 6  (4)
33
8  2 
2
5
0
 3

10 
6 
=

2
8

 1
4 3   0
1


0  7   3  1
5
0   4 2
2-0
-4-1
8-3
0-(-1) -7-1
1-(-4)
5-2
3-8
0-7

=
8
1
7




2 -5 -5
5 1 -8
5
3
-7

In matrix algebra, a real number is often called a SCALAR.
To multiply a matrix by a scalar, you multiply each entry in
the matrix by that scalar.
 2
4
 4
0 
4( 2)


 1
 4( 4)
 8

 16
4(0) 

4( 1) 
0 

 4
 1
 2 
 0
 2   4


3   6
 1 4
 2 
 0  6
-2


 
-3 3
6 -5
-2(-3) -2(3)
-2(6)
-2(-5)
5 


 8 
 2  5 


3  (8) 
 
6 -6
 -12
10

Your Turn:
Go to
http://www.phschool.com/
Web code: ata-0201
Complete the quiz and email me
your results
[email protected]