matrix intro multiplication, Exercises of Mathematics

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Matrix Multiplication:

Matrix Multiplication: Matrices can also be multiplied together. Since each matrix represents an array of data, tules for multiplying them together depend on the position of each entry. Consider the following example. At the beginning of November a stomach virus hits Central High School. Students in the Freshman and Sophomore classes are either well, a little sick, or really sick. The following tables show Freshmen and Sophomores according to their levels of sickness and their gender. Student Population % of Sick Students Categories Male ‘Female Categories Freshmen Sophomores Freshmen 250 300 Well 20% 25% Sophomores 200 275 Little Sick 50% 40% Really Sick 30% 35% Suppose school personnel needed to prepare a report and include the total numbers of well and sick male Freshmen and Sophomores in the school. well Freshmen males + well Sophomore males = well males (.2)(250) + (.25)(200) = 100 a little sick Freshmen males + a little sick Sophomore males =a little sick males (5)(250) + (.4)(200) = 205 really sick Freshmen males + really sick Sophomore males = really sick males (.3)(250) + (.35)(200) = 145 Notice the positions of the values in these products. We are multiplying rows by columns to get the information we want. Translating the tables to matrices and using the rows by columns pattern of multiplication we get the following result FS M F M F W|.2 .25 F1250 300] [(2)(250) + (25)(200) (.2)(300) + (.25)(275)] {100 128.75 L|5 4 love msl (5)(250) + (.4)(200) (.5)(300) + (.4)(275) |=L}205 260 Ri3 35 (-3)(250) + (.35)(200) (-3)(300) + (-35)(275) |r} 145 186.25 FS M F Mee W[100 128.75 W)2 25 F[250 300 _ £/205 260 L154)" ol o09 75 R\ 145. 186.25 Ri3 35