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 6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships related in a network.  7. Multiply matrices.

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Presentation on theme: " 6. Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships related in a network.  7. Multiply matrices."— Presentation transcript:

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2  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.

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

4 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

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

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

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

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10 ADDITIVE INVERSE OF A MATRIX:

11 Find the additive inverse:

12  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


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