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4.2 Matrix Multiplication Objectives: Multiply 2 matrices. Use matrix multiplication to solve mathematical and real-world problems. Standard: 2.8.11.1 Use matrices to organize and manipulate data, including matrix multiplication.
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MATRIX MULTIPLICATION INVOLVES MULTIPLICATION AND ADDITION.
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EX. 1
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*Let * Find AB, if it exists. * Find BA, if it exists. and
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* Let and * Find AB, if it exists. * Find BA, if it exists.
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* Let and * Find AB, if it exists.
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MATRIX MULTIPLICATION IS NOT COMMUTATIVE!!
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PSSA WARM-UP QUESTION Algebra II - Chp. 4 Standard 2.8.11 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?
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Standard 2.8.11 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?
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*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?
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Standard 2.8.11 I Use Matrices. What are the dimension requirements for matrix multiplication? What are the dimensions of a product matrix? Is matrix multiplication commutative?
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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.
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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?
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