Explanation Given Information: The Left Coast Bookstore chain in January sold 700 hardcover books, 1300 soft cover books, and 2000 plastic books in San Francisco; it sold 400 hardcover, 300 softcover and 500 plastic books in Los Angeles. Hardcover books sell for $ 30 each, softcover books sell for $ 10 each, and plastic books sell for $ 15 each. Formula Used: Multiplication of Matrices: If A is an m × n matrix and B is an n × k matrix, then the product A B is the m × k matrix whose i j th entry is the product ( A B ) i j = [ a i 1 a i 2 a l i 3 ... a i n ] [ b 1 j b 2 j b 3 j . . . b n j ] = a i 1 b 1 j + a i 2 b 2 j + a i 3 b 3 j + ... + a i n b n j Calculation: It is provided that the Left Coast Bookstore chain in January sold 700 hardcover books, 1300 soft cover books, and 2000 plastic books in San Francisco. Total number of sold hardcover are 400 , 300 softcover and 500 plastic books in Los Angeles. Hardcover books sell for $ 30 each, softcover books sell for $ 10 each, and plastic books sell for $ 15 each. Three prices and three quantities are provided. So, first form two matrices, one row and one column as: The price matrix (row matrix) can be constructed as: [ 30 10 15 ] For the quantity matrix, two types of quantities are provided. So, the matrix will be of the order 2 × 3 where the first row will represent the books sold in San Francisco, and the second row will represent the books sold in Los Angeles. The Quantity matrix can be constructed as: [ 700 1300 2000 400 300 500 ] Now, total cost can be calculated as: Cost=Quantity×Price Substitute the respective matrices obtained as: C = [ 700 1300 2000 400 300 500 ] [ 30 10 15 ] Here, A = [ 700 1300 2000 400 300 500 ] and B = [ 30 10 15 ]

7th Edition

ISBN: 9781337280426

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements ar…

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Chapter 4.2, Problem 57E

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To calculate: The column matrix and show how matrix multiplication (using the sales and price data matrices) may be used to compute the total revenue at the two stores if hardcover books sell for $30 each, softcover books sell for $10 each, and plastic books sell for $15 each.

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Chapter 4.2, Problem 56E

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The column matrix and show how matrix multiplication (using the sales and price data matrices) may be used to compute the total revenue at the two stores if hardcover books sell for $ 30 each, softcover books sell for $ 10 each, and plastic books sell for $ 15 each.

Solution Summary: The author shows how matrix multiplication may be used to compute the total revenue at the two stores if hardcover books sell for 30 each.

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To calculate: The column matrix and show how matrix multiplication (using the sales and price data matrices) may be used to compute the total revenue at the two stores if hardcover books sell for $30 each, softcover books sell for $10 each, and plastic books sell for $15 each.

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