Example 35Solve the simultaneous equations with 3 unknowns using MatricesExample 362x0y0z0502x0Z006x03y 02z 003A worker assembles a particular model of laptop, printer, modem and router.She assembles• two laptops, five printers, three modems and one router in 167 minutes• four laptops and ten printers in 240 minutes• six printers, twelve modems and three routers in 273 minutes. five modems and two routers in 82 minutesLet a = the amount of time in minutes it takes her to assemble one laptop.Let b= the amount of time in minutes it takes her to assemble one printer.Let c= the amount of time in minutes it takes her to assemble one modem.Let d= the amount of time in minutes it takes her to assemble one router.Write four simultaneous equations in terms of a, b, c and d.bWrite the simultaneous equations in matrix form.c Solve the matrix equation and hence find how long it takes her to assemble each of the four items.29 | Page Example 33Which of the following matrix equations have no solution?a) ²310=129-Example 34Solve the simultaneous equations by hand:Step 1: write the equations in matrix formb) [¹73]=[³3]3x+4y=132x+3y=9Step 2: Do the equations have a unique solution? Explain.Step 3: Solve the equations using matrix methods27|Page

Answered: Image /qna-images/answer/0aa69b5f-d1e7-40c3-84a7-a2813db4fa09.jpg

Answered: ar model of laptop, printer, three…

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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One hundred liters of a 50% solution is obtained by mixing a 60% solution with a 20% solution. Use a system of linear equations to determine how many liters of each solution are required to obtain the desired mixture. Solve the system using matrices.
Agriculture A fruit grower raises two crops, apples and peaches. The grower ships each of these crops to three different outlets. In the matrix A=12510075100175125 aij represents the number of units of crop i that the grower ships to outlet j. The matrix B=3.506.00 represents the profit per unit. Find the product BA and state what each entry of the matrix represents.
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.
A manufacture produce three models of a product and ships them to two warehouse. In the matrix A=[200300600350250400] aij represent the number of units model i that the manufacturer ships to warehouse j. The matrix B=[12.509.0021.50] Represent the price of the three models in dollars per unit. Find the product BA and state what each entry of the matrix represents.
Use matrix methods to solve each problem Nutritional planning One ounce of each of three foods has the vitamin and mineral content shown in the table. How many ounces of each must be used to provide exactly 22 milligrams mg of niacin, 12 mg of zinc, and 20 mg of vitamin C? Food Niacin Zinc Vitamin C A 1 mg 1 mg 2 mg B 2 mg 1 mg 1 mg C 2 mg 1 mg 2 mg

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