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
a21
a12
a22
 a1n
 a2 n

am1


 amn
am 2
Augmented Matrix
3x 4 y
2x 3y
6
5
3
2
4
3
6
5
Coefficient Matrix
3
2
4
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
0 1
0 0
1
1
4 10
1
2
Row Operations
Row Operations
1) Interchange any two rows
Ex: R1 R2
4 3
2 2
3 4
5
0
8
6
1 13
2) Replace a row by a nonzero multiple of that row
Ex: R2 1 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.
4 5
0
6
3 R3
1
0
4
3
2
1 10
2
1
3
6 12
2 0
2
1
2r2 r3
8
3
R1
7
R3
1
r1
2
3r2 r3
Row Operations
Apply the indicated row operation(s) to the matrix given.
4
2
3
0
2
5
6
6 3
7
0
R1
R2
R1
1
R2
R3
2r1 r2
5r1 r3
2
R1
R2
r3 r1
r3 r2
1
r1
3
1
3
7
9
7
8
19
10
5
2
6
10.2a Matrices
YKK - Yoshida Kogyo Kabushikikaisha
What 3-letter code appears on most zippers???