Ch. 12 Vocabulary
1.) matrix
2.) element
3.) scalar
4.) scalar multiplication
Column 1
Column 2 Column 3 Column 4
 a11 a12 a13 a14 

a
a22 a23 a24 
Row 2  21
a32 a33 a34 
Row 3  a31





Row m 
a
a
a
a
mn
mn
mn 
 mn
Row 1
A matrix of m rows and n columns is called
a matrix with dimensions m x n.
 2 3 4 

1.) 
 1 1  

2

2 X 3
10 
3.)  
2
X
1

7
 
3

2.)  
 6
8
2
7
3 X 3
4.)  3 4
1 X 2
9

5
8 
 3 5 


3 0

1
 2.)
1.)  4
 0 3
4 



  0 


3 X 2
2 X 2
4.) 
2 
1X 2
 1 2 3


3.) 0 1 8
0 0 1
3 X 3
 5
5.)  
 
6.)  3
2X 1
1X 1
To add matrices, we add the corresponding
elements. They must have the same
dimensions.
 5 0
A

 4 1
 5  6 0  3
A+B 

 4  2 1 3 
6 3
B

2 3 
 1 3 


6 4 
 2 1 3 
0
2.) 



1 0 1
0
0 0

0 0
 2 1 3 


1 0 1
When a zero matrix is added to another
matrix of the same dimension, that same
matrix is obtained.
To subtract matrices, we subtract the
corresponding elements. The matrices must
have the same dimensions.
1

3.)  2
 3
 1 1
 2  1

 3  2
2

0
1

1
1

 2
2  (1)   0


0  3    3
1  3   5
1

3
3 
3

3
4 
4 1 6 5
1.) 




6 3  7 3 
 2 6 


13 0 
1 3 2
 2 1 5   1 4 7 

2.) 
 



4 0 5 
6 4 3  2 4 8 
Scalar Multiplication:
2k 3k 
1 2 3
 1k




k  1 2 3  1k 2k 3k


 4 5 6
 4k 5k 6k 
We multiply each # inside our matrix by
k.
 3 0   9 0 

1.) 3 


 4 5  12 15
1 2 x   5 10 5 x 




2.) 5  4 y 1   20 5 y
5


2
0 5 x   0 25 5 x 2 
ADDITIVE INVERSE OF A MATRIX:
1
A
3
0 2

1 5 
 1
A  

3

0 2 

1 5
Find the additive inverse:
 2 1 5   2 1 5

 6 4 3  6 4 3 


 
 3x  1  4
1   26 0

2 








8
5

2

y
12
8








3x  4  1  1 26 0
2




 8  2 5  y  12 8
0  26 0
3x  4
2




5  y  12 8
 6
Scalar Multiplication:
0  26 0
6 x  8

 12



10  2 y  12 8

6x+8=26
6x=18
x=3
10-2y=8
-2y=-2
y=1
• Associative Property of Addition
(A+B)+C = A+(B+C)
• Commutative Property of Addition
A+B = B+A
• Distributive Property of Addition and
Subtraction
S(A+B) = SA+SB
S(A-B) = SA-SB
• NOTE: Multiplication is not included!!!