Its sales in January were as follows: 600 hardcover books, 1,300 softcover books, and 1,900 plastic books sold in San Francisco, and 300 hardcover, 200 softcover, and 400 plastic books sold in Los Angeles. The bookstore chain actually maintained the same sales figures for the first 6 months of the year. Each month, the chain restocked the stores from its warehouse by shipping 500 hardcover, 1,500 softcover, and 1,500 plastic books to San Francisco and 500 hardcover, 500 softcover, and 500 plastic books to Los Angeles. (a) Use matrix operations to determine the total sales over the 6 months, broken down by store and type of book.

For January, we can write the sales in matrix form for both the stores, where the first row corresponds to sales for San Francisco and the second row corresponds to sales for Los Angeles. The first column represents number of hardcover books sold, the second column represents the number of softcover books sold and the third column refers to the number of plastic books sold. So the sales matrix(S) for January is:

S = [tex]\left[\begin{array}{ccc}600&1300&1900\\300&200&400\end{array}\right][/tex]

Given that the bookstore maintained the same sales figure for the first six months of the year (i.e. January till June), the total sales for the six months can be calculated by multiplying the matrix S with 6. So the total sales (TS) matrix is:

TS = 6 x S

= 6 x [tex]\left[\begin{array}{ccc}600&1300&1900\\300&200&400\end{array}\right][/tex]

TS = [tex]\left[\begin{array}{ccc}3600&7800&11400\\1800&1200&2400\\\end{array}\right][/tex]

The first row of the matrix corresponds to the sales in San Francisco and the second row corresponds to the sales in Los Angeles.

The first column of the matrix shows the number of hardcover books sold in each of the stores, the second column shows the number of softcover books sold and the third column shows the number of plastic books sold.