http://www.ck12.org Chapter 8. Systems and Matrices
A=
0 − 1 8
1 2 0
4 3 12
, B=
1 5 1
2 2 1
4 3 0
Solution:
AB=
30 22 − 1
5 9 3
58 62 7
BA=
9 12 20
6 5 28
3 2 32
Example C
Compute the following matrix arithmetic: 10·( 2 A− 3 C)·B.
A=
[1 2
4 5
]
,B=
[0 1 2
4 3 2
]
,C=
[12 0
1 3
]
Solution: When a matrix is multiplied by a scalar (such as with 2A), multiply each entry in the matrix by the scalar.
2 A=
[ 2 4
8 10
]
− 3 C=
[− 36 0
− 3 − 9
]
2 A− 3 C=
[−34 4
5 1
]
Since the associative property holds, you can either distribute the ten or multiply by matrixBnext.
( 2 A− 3 C)·B=
[ 16 − 22 − 60
4 8 12
]
10 ·( 2 A− 3 C)·B=
[ 160 − 220 − 600
40 80 120
]
Concept Problem Revisited
The main difference between matrix algebra and regular algebra with numbers is that matrices do not have the
commutative property for multiplication. There are other complexities that matrices have, but many of them stem
from the fact that for most matricesAB 6 =BA.
Vocabulary
Matrix operationsare addition, subtraction and multiplication. Division involves a multiplicative inverse that is not
discussed at this point.