A drug production company has three branches A, B, and C, each of which produces two types of medicine daily. If the first branch produces 100 boxes of the first type, 400 boxes of the second type, and the branch B produces 200 boxes of the first type, 300 boxes of the type The second and branch C produce 150 boxes of the first type, 250 boxes of the second type. A) Systems the data in a matrix in two ways B) Are the two matrices equal? Why?

A drug production company has three branches A, B, and C, each of which produces two types of medicine daily. If the first branch produces 100 boxes of the first type, 400 boxes of the second type, and the branch B produces 200 boxes of the first type, 300 boxes of the type The second and branch C produce 150 boxes of the first type, 250 boxes of the second type. A) Systems the data in a matrix in two ways B) Are the two matrices equal? Why?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.1: Matrix Operations

Problem 19EQ: A factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two...

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Referring to Exercise 19, suppose that the unit cost of distributing the products to stores is the same for each product but varies by warehouse because of the distances involved. It costs $0.75 to distribute one unit from warehouse 1 and $1.00 to distribute one unit from warehouse 2. Organize these costs into a matrix C and then use matrix multiplication to compute the total cost of distributing each product.
A factory manufactures three products (doohickies, gizmos, and widgets) and ships them to two warehouses for storage. The number of units of each product shipped to each warehouse is given by the matrix A=[20015010075100125] (where aij is the number of units of product i sent to warehouse j and the products are taken in alphabetical order). The cost of shipping one unit of each product by truck is $1.50 per doohickey, $1.00 per gizmo, and $2.00 per widget. The corresponding unit costs to ship by train are $1.75, $1.50, and $1.00. Organize these costs into a matrix B and then use matrix multiplication to show how the factory can compare the cost of shipping its products to each of the two warehouses by truck and by train.
In general, it is difficult to show that two matrices are similar. However, if two similar matrices are diagonalizable, the task becomes easier. In Exercises 38-41, show that A and B are similar by showing that they are similar to the same diagonal matrix. Then find an invertible matrix P such that .