1. Warm-up
3.)

2. Multiplying Matrices

3. In order to multiply matrices...
A • B = AB
r x c
r x c
r x c
the inside dimensions must be the same!
Ex 1.
Can you multiply? What will the dimensions be? A B AB
2 x 3
3 x 4
2 x 4 AB A B
5 x 3
5 x 2
Not possible

4. Identify the dimensions of each matrix
Identify the dimensions of each matrix. Then, tell if it is possible to multiply them together.

5. The #1 Jam in the ATL The Matrix Song
To the tune of “My Darling Clemintine”

6. Multiply them line by line
The Matrix Song
Row by column, row by column
Multiply them line by line
Add them up to form a matrix
Now you’re doing it just fine

7. How to multiply... ac ad =
2 x 1
1 x 2
2 x 2

8. How to multiply... ac ad = bc bd
2 x 1
1 x 2
2 x 2

9. Ex. 1

10. sum of pair-wise products
How to multiply... ag
+bi
+ck ah
+bj
+cm =
2 x 3
3 x 2
2 x 2
sum of pair-wise products

11. sum of pair-wise products
How to multiply... ag
+bi
+ck ah
+bj
+cm = dg
+ei
+fk dh
+ej
+fm
2 x 3
3 x 2
2 x 2
sum of pair-wise products

12. Ex. 2

13. -1(4) +5(6) -1(-3) +5(8) -4 + 30 3 + 40 5(4) +2(6) 5(-3) +2(8) 20 +12
Ex. 3
-1(4)
+5(6)
-1(-3)
+5(8) -4
+ 30 3
+ 40
5(4)
+2(6)
5(-3)
+2(8) 20
+12
-15
+ 16 =
+ -24
+ -32
0(4)
+-4(6)
0(-3)
+-4(8) 26 43 32 1
-24
-32

14. Ex. 4
Find AB
-16
+ 1
-12 +2
-15
-10 =
- 2
- 4 -2
- 4