Exam 4: Matrices

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 $16,400, and risk factors make it prudent to invest some money in all three investments. What is the minimum amount that will be invested at 7%, and in this case how much will be invested at the other rates? ​

Evaluate the determinant. ​ ​

Suppose a simple economy with only an agricultural industry and a steel industry has the following technology matrix. ​ ​ If surpluses of 15 units of agricultural products and 34 units of steel are desired, find the gross production to the nearest unit of each industry. ​

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. ​ ​ ​

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 matrices to find BE, if possible. ​ ​

An economy has a manufacturing industry and a banking industry. Each unit of manufacturing output requires inputs of 0.5 unit of manufacturing and 0.2 unit of banking. Each unit of banking output requires inputs of 0.3 unit each of manufacturing and banking. If surpluses of 133 units of manufacturing and 100 units of banking are desired, find the gross production of each industry. ​

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the greatest improvement in rank? 1995 2002 ​

A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 2 blocks of common stock, 1 municipal bond, and 3 blocks of preferred stock. A customer wants 16 blocks of common stock, 8 municipal bonds, and 6 blocks of preferred stock. Let x equal the number of units of Portfolio I, y equal the number of units of Portfolio II, and z equal the number of units of Portolio III. If the numbers of the three portfolios offered must be integers, find the general solution that can be used to determine all possible offerings. ​

Multiplication by a matrix can be used to encode messages (and multiplication by its inverse can be used to decode messages). Given the code and the code matrix , use matrix A to encode the message "To be or not to be." ​

An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input. If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry. ​

The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Write a matrix A that contains the number of each of these species in the United States in 2003 and a matrix B that contains the number of each of these species outside the United States in 2003. ​ ​United States ​Foreign ​ ​

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 A can carry 2300 cu ft and 23,000 lb, how many of each product can it carry? ​

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

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 0.2 unit of computers. Each unit of computer industry output requires inputs of 0.8 unit of electronic components and 0.1 unit of computers. Write the technology matrix for this simple economy. (E, electronics components industry; C, computer industry) ​

Use the matrices below. Perform the indicated operations. ​ I·F·Z ​

For , are FFT and F^TF defined?

Write a zero matrix that is the same order as D. ​ ​ ​

An economy has a manufacturing industry and a banking industry. Each unit of manufacturing output requires inputs of 0.4 unit of manufacturing and 0.1 unit of banking. Each unit of banking output requires inputs of 0.3 unit each of manufacturing and banking. Write the technology matrix for this economy. (M, manufacturing industry; B, banking industry) ​

The inverse of matrix A is given. Use the inverse to solve for X. ​ Solve . ​