 6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships related in a network.  7. Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.  8. Add, subtract, and multiply matrices of appropriate dimensions.  9. Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

 Addition  Augmented Matrix  Element  Equation  Matrix Multiplication  Scalar Multiplication  Variable Matrix  Zero Matrix

A matrix of m rows and n columns is called a matrix with dimensions m x n. 2 X 3 3 X 3 2 X 1 1 X 2

To add matrices, we add the corresponding elements. They must have the same dimensions. A + B

When a zero matrix is added to another matrix of the same dimension, that same matrix is obtained.

To subtract matrices, we subtract the corresponding elements. The matrices must have the same dimensions.

ADDITIVE INVERSE OF A MATRIX:

Find the additive inverse:

 Lab,in class, with a partner (one), finish in class- do at end. Do as much as you can. You and your partner many turn in one paper, both names. Textbook p. 181 #1-6; need to learn how to use calculator with matrices.  At home: textbook page: 172 #27 all parts, due next class