1. 4.2 Adding and Subtracting Matrices 4.3 Matrix Multiplication
Date: _____________

2. Adding and Subtracting Matrices
Must be the same dimensions
Add or Subtract corresponding elements

3. Adding Matrices
To add matrices, add all the corresponding elements. 4 -2 7 3 2 5 -3 7 + = 12 -3

4. − = 4 -2 7 3 2 5 -3 1 -4 2 3 Subtracting Matrices
To subtract matrices, subtract all the corresponding elements. 4 -2 7 3 2 5 -3 1 -4 − = 2 3

5. 12 -4 13 -7 -8 19 23 14 20
-23 − =
-10
-21

6. Dimensions are not the same.12 -2 4 7 − = 9 -3
Not Possible!
Dimensions are not the same.

7. Solving a Matrix Equation
Get the variable by itself
The variable is representing a matrix
Subtracting matrices

8. Solving a Matrix Equation
Subtracting matrices 4 -8 -1 -1 11 1

9. Solving Equation Matrices
Each corresponding element is equal

10. Muliplying Matrices Same concept as the Distributive Property
Scalar Multiplication – multiply a matrix by a factor. 45
-36 30 60
-30 21
Same concept as the Distributive Property

11. Matrix Multiplication
Suppose that you want to multiply matrices
A and B. A has dimensions m x n and B has
dimensions p x q.
If multiplication is possible, the answer will have dimensions m x q.
m x n
p x q
If n = p,
multiplication is possible.

12. multiplication is possible.2 9 5 8 7 8 2 3
answer will be 2 x 2
2 x 2
2 x 2
multiplication is possible. 28 43
(2)(8) + (9)(3)
(2)(5) + (9)(2) = 51 80
(7)(5) + (8)(2)
(7)(8) + (8)(3)

13. DON’T FORGET YOUR CALCULATOR!!!
FUN?
DON’T FORGET YOUR CALCULATOR!!!