10.2a Matrices
Philadelphia and Forrest Gump
Tom Hanks won the Oscar for best leading actor two years
in a row. What were the titles of the two movies?
Matrices
A matrix is defined as a rectangular array of numbers.
 a11
a
 21
 

am1
3x  4 y  6

2x  3y  5

a12
a22

am 2
 a1n 
 a2 n 
 

 amn 
Augmented Matrix
Coefficient Matrix
3 4 6 


2
3
5


3 4 


2 3

Matrices
Write an augmented matrix from the following system.
x  3y  3z  4

2x  3y  z  15

4 x  3y  z  19
Write the system of equations that corresponds to the augmented
matrix and solve.
1
1 1 1
0 1  4 10 


0 0 1  2
Row Operations
Row Operations
1) Interchange any two rows
Ex: R1  R2
4 3  5  8
2 2 0

6


3 4  1 13 
 2) Replace1a row by a nonzero multiple of that row
Ex: R2  r2
2
3) Replace a row by the sum of that row and a constant nonzero
multiple of another row.
Ex: R2  4r1  r2
Row Operations
Apply the indicated row operation(s) to the matrix given.
6
 4 5 0
 1 0  4  3 R  2r  r
2
3

 3
 3 2  1 10 

 2  6 12 8 
 1  2 0  3


 3 2  1 7 

1
R1  r1
2
R3  3r2  r3




















Row Operations
Apply the indicated row operation(s) to the matrix given.
5 6
 4 2
  3 0  6 3 R  R
2

 1
 2  7 0 1







R1  r3  r1 

R2  r3  r2 








1
 R1   r1
3



 R  2r  r
1
2
 2

 R3  5r1  r3

 













 2  7  8 5 
1

9
19

2


  3  7  10 6 
10.2a Matrices
YKK - Yoshida Kogyo Kabushikikaisha
What 3-letter code appears on most zippers???