Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the change in sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) from 2004 to 2005. ;
B)
C)
E)

Question

Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the change in sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) from 2004 to 2005. ​  ​   ;  ​
B) ​ 
C) ​ 
E) ​

Quizplus · Accepted Answer

To find the change in sales, we need to subtract the 2004 sales (matrix A) from the 2005 sales (matrix B). However, we only want to consider the change in sales by type and city, so we need to subtract the corresponding elements (i.e. the wholesale sales for each city and the retail sales for each city). Thus, the matrix that represents the change in sales is:

B - A = [ [24 16 -7] [-6 18 0] [12 14 -11] ]

where the first row corresponds to Chicago, the second row corresponds to Atlanta, and the third row corresponds to Memphis. The first column corresponds to wholesale sales, and the second column corresponds to retail sales. Therefore, the correct answer is B.

Let Matrix a Represent the Sales (In Thousands of Dollars)