Algebra 2/Trig 4.2 Matrix Multiplication
p. 225
Learning Targets: Multiply two matrices.
Use matrix multiplication to solve mathematical and real-world
problems.
MATRIX MULTIPLICATION:



To Add or Subtract matrices the dimensions must be the same (row by column)
We cannot divide matrices
We can multiply matrices – with rules.
EXAMPLE 1:
[5 2
7
−1] 𝑥 [ 1 ] =
−2
The first matrix has dimensions of 1 x 3, the second matrix has dimensions of 3 x 1.
Outer dimensions
RULE:
1x3 • 3x1
Inner dimensions
The INNER dimensions must be the same to multiply the matrices.
The OUTER dimensions give the dimensions of the product matrix
EXAMPLE 2: Find J x K, if possible.
2 −4
𝐽= [
] ,
3 0
𝐾= [
5 −4
]
1 3
Check the dimensions. They are: 2 x 2 and 2 x 2. The inner dimensions are the ______________ so we
______________ multiply the two matrices.
What are the dimensions of the product matrix? ______________________
1
We will multiply “Row by Column”.
2 −4
5
JK = [
]𝑥 [
3 0
1
−4
]=
3
Find KJ
2 −4
5 −4
KJ = [
]x[
]=
3 0
1 3
Is matrix multiplication always commutative?
EXAMPLE 3:
3 −1
Let M = [
4 0
5
]
−2
3 5 4
Let N = [−1 6 7 ]
2 0 −4
Find the dimensions of the matrices and determine if it is possible to find MN. If so, find MN.
NOTE: When using a calculator to find MN you do not need the multiplication sign (x) between the
matrices. [𝑀][𝑁]
MN =
Homework: 4.2 pages 229 – 231 Problems 7 – 14 - Do not use a calculator, by hand.
Problems 15 -20 ALL and 24 – 26 ALL, you may use a calculator.
2