Transcript matrix - ALS Schools

Chapter 4: Matrices
Lesson 1: using Matrices to Represent
Data
 Objectives:
– Represent mathematical and real-world data in
a matrix.
– Find sums and differences of matrices and the
scalar product of a number and a matrix.
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
 6 2  1
 2 0 5 


8
0

 10
1
0
4
3
2 
 3
 2
1

 7
0
4
1
0

1
3
3x3
9
5 7
1x4
6
5 9
2
7
 1

2
(or square
matrix)
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


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)

20
 5

 4
 3
2
05
33
5
0
47 

6  (4)
8  2 
 3

10 
6 
=

2
8

 1
4
0
5
3 0
1


 7   3  1
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

Assignment 1
• Ch.4.1 pg.221 # 6 to 9, 12 to 14,
and 19 to 23.
•Due date: Sept. 30th, 2009
•To: Mr. Mohammed Akour
•By email:
[email protected]
This presentation edited by
Mr. Mohammed Akour
Mr Wassim Fakih
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