4.2 Adding and Subtracting Matrices 4.3 Matrix Multiplication

1. 4.2Adding and Subtracting Matrices4.3Matrix Multiplication Date: _____________

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

3. 4 -2 3 2 7 0 5 -3 Adding Matrices To add matrices, add all the corresponding elements. 7 0 + = 12 -3

4. 4 -2 3 2 7 0 5 -3 Subtracting Matrices To subtract matrices, subtract all the corresponding elements. 1 -4 − = 2 3

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

6. 0 7 -2 4 12 − = 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 Scalar Multiplication – multiply a matrix by a factor. 45 -36 30 0 0 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. 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. FUN? DON’T FORGET YOUR CALCULATOR!!!