# The companys purchases in advertising for the n

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. The company’s purchases in advertising for the n channels is given by c , so summing up the entries of c gives the total amount of money the company spends across all channels. (b) v = Rc . To find the total number of impressions v i in the i th market segment, we need to sum up the impressions from each channel, which is given by an inner product of the i th row of R and the amounts c spent on advertising per channel. (c) a T v = a T Rc . The total profit is the sum of the profits from each market segment, which is the product of the number of impressions for that segment v i and the profit per impression for that segment a i . The total profit is the sum i a i v i = a T v . Substituting v = Rc gives a T v = a T Rc . (d) argmax j R 3 j , i.e. , the column index of the largest entry in the third row of R . The number of impressions made on the third market segment, for each dollar spent, is given by the third row of R . The index of the greatest element in this row is then the channel that gives the highest number of impressions per dollar spent. (e) The fifth channel makes relatively few impressions on the third market segment per dollar spent, compared to the other channels.
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6.14 Columns of difference matrix. Are the columns of the difference matrix D , defined in (6.5General examplesequation.6.4.5), linearly independent?
7.3 Trimming a vector. Find a matrix A for which Ax = ( x 2 , . . . , x n - 1 ), where x is an n -vector. (Be sure to specify the size of A , and describe all its entries.)