Exam 3: Matrices

Suppose an economy has the technology matrix below. If surpluses of 525 units of electronics, 31 units of steel, and 140 autos are desired, find the gross production for each industry. ​ ​ ​

Use determinants to decide whether the matrix has an inverse. ​

Suppose a primitive economy consists of two industries, farm products and farm machinery. Suppose also that its technology matrix is ​ If surpluses of 97 units of farm products and 18 units of farm machinery are desired, find the gross production of each industry. ​

If and , does ?

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.

Use the following matrices to perform the indicated matrix operations, if possible. ​ ​ ; ​

When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. What payment plan did Maxx Industries use if the outstanding debt is given by the following matrix?

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. ​

Set up the system of equations and then solve it by using inverse matrices. ​ Bee ancestry Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number of ancestors of a male t + 2 bee generations before the present generation is the sum of the number of ancestors t and t + 1 generations before the present. If the numbers of ancestors of a male bee in a given generation t and in the previous generation are given by , then there is a matrix M such that the numbers of ancestors in the two generations preceding generation t are given by . ​ For a given male bee, the numbers of ancestors 5 and 6 generations back are given by . ​ Find the numbers of ancestors 4 and 5 generations back by multiplying both sides of by the inverse of M. ​

Use the matrices to find CF, if possible. ​ ​ ​ ​

A trust account manager has $220,000 to be invested. The investment choices have current yields of 8%, 7%, and 10%. Suppose that the investment goal is to earn interest of $16,600, and risk factors make it prudent to invest some money in all three investments. If $30,000 is invested at 10%, how much will be invested at each of the other rates? ​

Use the matrices to find BE, if possible. ​ ​

Use matrix A to find A³, if possible. ​ ​

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Use a matrix operation to find the change from 1995 to 2002 in rank for each breed and in registration numbers for each breed. ​

Use the following matrices to perform the indicated matrix operations, if possible. ​ ​ ; ​

The following technology matrix for a simple economy describes the relationship of certain industries to each other in the production of 1 unit of product. ​ ​ For each 100 units of manufactured products produced, how many units of fuels are required? ​

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

Set up the system of equations and then solve it by using inverse matrices. Transportation The Ace Freight Company has an order for two products to be delivered to two stores of a company. The table below gives information regarding the two products. If truck B can carry 2250 cu ft and 20,000 lb, how many of each product can it carry? ​

Evaluate the determinant. ​ ​

Use matrix F to find F², if possible. ​ ​