Example 19 - Chapter 3 Class 12 Matrices

Transcript

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