4.2 Matrix Multiplication Objectives: Multiply 2 matrices. Use matrix multiplication to solve mathematical and real-world problems. Standard: 2.8.11.1.

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4.2 Matrix Multiplication Objectives: Multiply 2 matrices. Use matrix multiplication to solve mathematical and real-world problems. Standard: Use matrices to organize and manipulate data, including matrix multiplication.

MATRIX MULTIPLICATION INVOLVES MULTIPLICATION AND ADDITION.

EX. 1

*Let * Find AB, if it exists. * Find BA, if it exists. and

* Let and * Find AB, if it exists. * Find BA, if it exists.

* Let and * Find AB, if it exists.

MATRIX MULTIPLICATION IS NOT COMMUTATIVE!!

PSSA WARM-UP QUESTION Algebra II - Chp. 4 Standard D Model Situations.  How is the size of a matrix determined? How can the location of an individual entry be identified? How can matrices be used to model situations?

Standard I Use Matrices. Attendance data at aquarium shows are in the tables below. The data in each table can be written in a matrix. Each matrix will have 3 rows and 2 columns, so the dimensions of each matrix will be 3 x 2. *1). Arrange the data from the first table in matrix A; arrange the data from the second table in matrix B. *2). How many morning Dolphin Show customers were there altogether? How many Shark Show customers were there altogether?

*3). How many more people attended each show on Saturday than the corresponding show on Sunday? *4). Suppose every customer received 2 coupons for beverages. How many coupons were given out at each show?

Standard I Use Matrices. What are the dimension requirements for matrix multiplication? What are the dimensions of a product matrix? Is matrix multiplication commutative?

Writing Activities: 3). Which pair (s) of the matrices above can be added? Explain. 4). Which pair(s) of the matrices above can be multiplied? Explain.

Writing Activities 5). For the given matrices, does AC equal CA? Explain. 6). What must be true of matrix M in order for you to be able to find M 2 ? 7). What are some of the differences between addition and multiplication of matrices and addition and multiplication of real numbers?