Download 4.3 Multiplying matrices - Central Dauphin School District

4.3 MULTIPLYING MATRICES

You can multiply matrices if and only if:
the number of columns in the first matrix is the
same as the number of rows in the second matrix

Ex:
A5 x 3 and B3 x 4 = AB
5x4

If the matrices cannot be multiplied =
product matrix is not defined
MULTIPLYING MATRICES
𝑤 𝑥
𝑎𝑤 + 𝑏𝑦
𝑎 𝑏
X
=
𝑦
𝑧
𝑐𝑤 + 𝑑𝑦
𝑐 𝑑
𝑎
Step 1:
𝑐
𝑤
𝑏
x 𝑦
𝑑
𝑥
𝑧
𝑎
Step 2 :
𝑐
𝑤
𝑏
x 𝑦
𝑑
𝑥
𝑧
𝑎
Step 3 :
𝑐
𝑤
𝑏
x 𝑦
𝑑
𝑥
𝑧
𝑎
Step 4 :
𝑐
𝑤
𝑏
x 𝑦
𝑑
𝑥
𝑧
𝑎𝑥 + 𝑏𝑧
𝑐𝑥 + 𝑑𝑧
FIND RS IF
1. R =
3
−1
2
−2 5
and S =
0
1 7
AT A SWIMMING MEET 6 POINTS ARE AWARDED FOR
1ST PLACE, 4 POINTS FOR 2ND PLACE, AND 3 POINTS
FOR 3RD PLACE.
2. The chart shows how many swimmers placed in each position through the meet for
the four participating schools.
School
1st Place
2nd Place
3rd Place
Central Dauphin
4
7
3
Cumberland Valley
8
8
1
Hershey
10
5
3
Carlisle
3
3
6
Write a set of matrices to model the points earned.
Which team won the meet?
COMMUTATIVE PROPERTY – DOES IT
WORK FOR MATRICES?
1 2
3. Find each product if P = 4 3 and S = 9 −3 2
6 −1 −5
0 −1
a. PS
b. SP
DISTRIBUTIVE PROPERTY – DOES IT WORK
FOR MATRICES?
4. Find each product if A = 3
−1
a. A (B + C)
1 1
2
−2 5
B=
and C =
4
−5 3
6 7
b. AB + AC