Lesson Plan : Matrix Multiplication

Teacher Name:
 Chris Wild
 Grade 7-8

 Multiplying Matrices
 Identify matrix dimensions and determine whether the product is defined and if so, what the matrix product dimensions will be. Steps to multiply square and not square matrices with defined products. Multiplicative properties or matrices: commutative, distributive, associative
 Students will: understand whether two matrices can be multiplied (is the product defined), be able to determine what the dimensions of the product will be, perform the steps of multiplying two matrices, determine whether or not the multiplicative properties for real numbers apply to matrix multiplication.
 Given the dimensions of two matrices students should be able to determine whether the matrices can be multiplied, whether the product is defined. Given matrices whose product is defined students should be able to perform matrix multiplication showing each step of their work (important to be sure of proper signs and avoid computation errors). Splitting the class with one representative working at the board have one group find eeach side of the commutative, distributive, associative examples and determine whether the properties hold for matricx multiplication.
 Handout with definitions, examples and steps defined for matrix multiplication. Pencil, calculator as some products especially when testing associative property may be rather large.
 After a brief review of matrix terms, dimensions, and adding/subtracting matrices... show a table with the scoring summary for a football team over a season listing type and number of each scoring play (touchdown, XP, FG, 2-pt, Safety). This can be represented by column matrix R. The point values associated with each type of score can be organized into row matrix P. We can now use matrix multiplication to find the total points scored by the team for the entire year.
 NOTE: unlike addition, the matrices do not have to have the exact same dimensions. Explain that a product is defined if the number of columns of the first equals the number of rows of the second. If defined show how dimensions of product can be determined by dimension of matrices being multiplied. Review step by step sum of the row/column products using 2 x 2 square matrix example.
 Have students work through their own 2 x 2 example. Use a 3 x 2 matrix multiplied by 2 x 3 matrix to determine whether commutative applies. (what do the expected product dimension indicate?) EMPHASIS: encourage students to show all work which will allow them to identify computation errors.
 Real world examples: finish football point scoring example from beginning 1 x 5 matrix multiplied by 5 x 1 matrix gives 1 x 1 single answer of total points. Three teams two columns representing number of wins and ties respectively. Another matrix showing the points awarded for a win and a tie respectively, determine which team wins. Investigate 2 x 2 identity matrix.
Checking For Understanding:
 How do we determine whether the product of two matrices is defined? How can we determine what the dimensions of the product (if defined) will be? 2x2, 3x3 squares and 2x3 multiplied by 3x2 be sure students can identify the sequence of multiplying first row of first matrix by each column of second then work to the next row of first matrix, etc.
 Have students perform additional exercises to determine if defined, dimensions, then results for various matrices. Integrate more real world problems where matrices can be used. Example: School fundraiser, number of each items sold in a table, create a matrix, create corresponding matrix for price of each item, calculate total money made from the fundraiser.

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