Exam 4: Matrices

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Form a matrix for the 1995 data and a matrix for the 2002 data. ​ 1995 2002 ​

A car dealer can buy midsize cars for 11% under the list price, and he can buy luxury cars for 14% under the list price. The following table gives the list prices for two midsize and two luxury cars. ​ Write these data in a matrix and multiply it on the left by the matrix ​ ​ ​

Suppose the technology matrix for a closed model of a simple economy is given by ​ ​​ Find the gross productions for the industries. ​

A system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the following system, if a solution exists.

Write the augmented matrix associated with the system.

Use row operations on the augmented matrix to solve the given system of linear equations. ​ ​

The figure that follows depicts the mean (average) flow time for a job when the critical-ratio rule is used to dispatch workers at several machines required to complete the job. In the figure, WHN 1, WHN 2, and WHN 3 represent three different rules for determining when a worker should be transferred to another machine, and Where represents six rules for determining the machine to which the worker is transferred. Construct a 3×6 matrix A to represent these data, with entries rounded to the nearest integer. ​ ​

A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the system, if one exists.

Using the matrices A and B below, what condition must be satisfied in order that AB and BA are defined? ​ and

A simple economy has an electronic components industry and a computers industry. Each unit of electronic components output requires inputs of 0.3 unit of electronic components and 0.6 unit of computers. Each unit of computer industry output requires inputs of 0.2 unit of electronic components and 0.2 unit of computers. If surpluses of 641 units of electronic components and 10 units of computers are desired, find the gross production to the nearest unit of each industry. ​

Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A. ​ ​ If surpluses of 40 agricultural units and 70 mineral units are desired, find the gross production to the nearest unit for each industry. ​

The following tables give the death rates, per 100,000 population, by age for selected years for males and females. If matrix M gives the male data and matrix F gives the female data, find matrix M - F and describe what it means. ​​ ​Males Females ​​ ​

Use the matrices to find , if possible. ​ ​

Find the inverse matrix, if one exists.

Suppose the development department of a firm charges 10% of its total monthly costs to the promotional department, and the promotional department charges 5% of its total monthly costs to the development department. The direct costs of the development department are $25,400, and the direct costs of the promotional department are $9,400. The solution to the matrix equation or the column matrix gives the total costs for each department. Note that this equation can be written in the form or , which is the form for an open economy. Find the total costs for each department in this (micro)economy. ​

Multiply the matrices. ​ ​

A system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the following system.

A system of linear equations and a reduced matrix for the system are given. Use the reduced matrix to find the general solution of the system, if one exists ​ ​​ ​​ ​

Find the inverse matrix, if one exists. ​

Use technology to find the determinant. ​ ​