4.2 Adding and Subtracting Matrices 4.3 Matrix Multiplication Date: _____________

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

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

− = 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

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

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

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

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

Solving Equation Matrices Each corresponding element is equal

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

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.

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)

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