What is 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 


What is the order?
8
0

 10
1
4
3
2 
 3
 2
1

 7
0
4
0
1
3
1
0

3x3
 1

2
9
1x4
6
5 9
2
(or square
matrix)
7
3

8
6 
2x2
3x5
(or square
matrix)
5
7
0
(Also called a
column matrix)
  9
7
 
0
 
6
4x1
(Also called a
row matrix)

Adding Two Matrices
To add two matrices, they must have the same order.
To add, you simply add corresponding entries.
 5  3  2 1 
 3 4    3

0

 

 0
7   4  3
8
 5

=
=


0
1
4
2
3


9
 1
5

7
5
3
3
2
 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


Subtracting Two Matrices
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

Multiplying a Matrix by a Scalar
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 

 1
 1
 2 
 0
 2   4


3   6
5 


 8 
8)
7)
10)
9)
11)
12)
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