Download 6.6 Basic Matrices Ops

The Algebra of Matrices
Matrix: An array of numbers.
Columns
3 2 5
A 2  3  

1 4 0
Matrix Name
(Capital Letter)
Matrix Size
(row x column)
Rows
Elements: arc
a22 = 4
Addition/Subtraction of Matrices:
• Two matrices can only be added/subtracted if they have the
same dimensions.
3+5=8
3 2 5
A 2  3  

1 4 0
5 4 1 
B 2  3  

3 0 2
Add the corresponding elements!

a811 a12
A  B  
a21 a22
a13 

a23 
Subtract the corresponding elements!
3 - 5 = -2
3 2 5
A 2  3  

1 4 0
-2
A  B  


5 4 1 
B 2  3  

3 0 2



Scalar Multiplication: Multiply each element in the matrix by
the real number.
(2x3=6)
3 2 5
A 2  3  

1 4 0

 6
2A  




Try This:
2 1


A  4 0 

3 5 

4 3


B  1 0

1 2



2A - B =
8 5
7 0 



5 8 

Multiplication of Matrices:
• Two matrices can only be multiplied if the number of
columns of the first matrix equals the number of rows in the
second matrix.
A23  B32  AB22
=
Product Dimensions
•The dimensions of the product matrix will then be the
number of rows from the first matrix by the number of
columns in the second.

2 0 3
A 23  
 B33
1 4 2
Example:
2 1 1 


 3 4 1

0 3 3

ab11 = Sum of products of elements from row 1 of matrix A with the
corresponding elements from column 1 of matrix B.


ab11 = (-2 x 2) + (0 x 3) + (3 x 0)
= -4
AB23
a- 4
 a

11
a12
21
a22

a

a

13
23
Example:
2 0 3
A 23  

1 4 2

Find BA:

B33
2 1 1 


 3 4 1

0 3 3

Example:
Find A2:

2 3
A  

4 1
Playing The Stock Market:
Three investors Kelsey, Nicole, and Linda each own a certain number of shares of
four stocks - McDonalds, Coke, Walmart, and AT&T.
Number of Shares of Stock
McDonalds Coke Walmart AT&T
Kelsey 50
100 30 25 


30
Nicole 100 150 10


Linda 
100 50 40 100

Current Value of Each Share
McDonalds
Coke
Walmart
AT&T
$ 20.37


$
16.21


$ 90.80


$ 42.75
Find each students’ current cash-in value for their stocks.


Kelsey  (50  20.37)  (100 16.21)  (30  90.80)  (25  42.75)
 $ 6,432.25
Nicole  (100  20.37) (150 16.21)  (10  90.80)  (30  42.75)
 $ 6,659
Linda  (100  20.37)  (50 16.21) (40  90.80)  (100  42.75)
 $ 10,754.50
Kelsey
Nicole
Linda

$6,432.25


$6,659.00
 
$10,754.50


