1. 4.2 MULTIPLYING MATRICES

2. DESCRIBING MATRIX PRODUCTS
To multiply matrices A and B, the # of
columns in A must match the # of rows in B
If A is m x n and B is n x p, AB will be m x p.
A ∙ B = AB
mxn nxp mxp
What will be the dimensions of AB if:
A is 2 x 3 and B is 3 x 4?
A is 3 x 2 and B is 3 x 4?

3. FINDING THE PRODUCT
For each entry in AB:
Multiply entries across the same row of A,
by those down the same column of B,
then add.
Example:

4. EXAMPLES:
 Find the product, if possible.

6. YOUR TURN!
Find AB if:

7. MATRIX MULTIPLICATION PROPERTIES:
Find AB if:
Now find BA.
Is matrix multiplication commutative?

8. MORE PROPERTIES:
Simplify each expression if:
1. A(B + C)
2. AB + AC
The distributive property is still true
for matrices!

9. YOUR TURN!
 Find B(A + C)

10. MATRIX EQUATIONS
 Justlike before:
 Simplify first (by multiplying)
 Write equations and solve.
Example: Solve for x and y.

11. YOUR TURN!
 Solve for x and y.