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Example 19 In a legislative assembly election, a political group hired a public relations firm to promote its candidate in three ways: telephone, house calls, and letters. The cost per contact (in paise) is given in matrix A as A = [■8( 40 @100@50)] The number of contacts of each type made in two cities X and Y is given by B = [■8(1000& 500 &5000@3000&1000&10,000)] Find the total amount spent by the group in the two cities X and Y. We need to calculate total amount spent by the group in two cities x & y Total amount spent = Number of contact × Cost per contact = BA = [■8(1000&500&5000@3000&1000&10,000)]_(2 × 3) [■8(40@100@50)]_(3 × 1) = [█(𝟏𝟎𝟎𝟎(𝟒𝟎)+𝟓𝟎𝟎(𝟏𝟎𝟎)+𝟓𝟎𝟎𝟎(𝟓𝟎)@𝟑𝟎𝟎𝟎(𝟒𝟎)+𝟏𝟎𝟎𝟎(𝟏𝟎𝟎)+𝟏𝟎,𝟎𝟎𝟎(𝟓𝟎))]_(𝟐 × 𝟏) = [█(40,000+50,000+250,000@120,000+100,000+500,000)] = [█(𝟑𝟒𝟎,𝟎𝟎𝟎@𝟕𝟐𝟎,𝟎𝟎𝟎)] Hence, total amount spent = [█(340,000@720,000)] Thus, Total amount spent by the group in city X = 340,000 paise = Rs. 3,400 Total amount spent by the group in city Y = 720,000 paise = Rs. 7,200 Note: We cannot do AB AB = [■8(40@100@50)]_(3 × 1) [■8(1000&500&5000@3000&1000&10,000)]_(2 × 3) Since, orders does not match, AB is not possible

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.