Exam 4: Matrices

​Using the data in the following tables, Let matrix A represent imports (in billions of dollars) to U.S. from country groupings, and let matrix B represent exports (in billions of dollars) from U.S. to country groupings. Find the total U.S. trade with these groupings by finding A + B. ​ ​

The following tables give the capital expenditures and gross operating costs of manufacturing establishments for pollution abatement, in millions of dollars. Which type of pollution abatement was most expensive in 2005? ​ ​Pollution Abatement Capital Expenditures ​Pollution Abatement Gross Operating Costs ​ ​

Use inverse matrices to find the solution of the system of equations. ​ ​

Write the transpose of matrix A. ​ ​

Use technology to solve the system of equations, if a solution exists.

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

From the data in the following table, make a matrix A that gives the value (in billions of dollars) of U.S. imports from the various country groupings in the years 2000 and 2002. ​ Imports to U.S. from Country Groupings ($billions) Exports from U.S. to Country Groupings ($billions) ​

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

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

Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. If ALCO pays 35% of the amount owed on each debt, write the matrix giving the remaining debts. ​ ​ ​

Find the inverse of matrix A and check it by calculating .

The given matrix is an augmented matrix used in the solution of a system of linear equations. What is the solution of the system?

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 $16,300, and risk factors make it prudent to invest some money in all three investments. What is the maximum amount that will be invested at 7%, and in this case how much will be invested at the other rates? ​

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

Use the indicated row operation to change matrix A, where . ​ Add times row 1 to row 3 of matrix A and place the result in row 3 to get 0 in row 3, column 1. ​

A poll of 3620 people revealed that of the respondents who were registered Republicans, 893 approved of the president's job performance, 257 did not, and 135 had no opinion. Of the registered Democrats, 142 approved of the president's job performance, 426 did not, and 501 had no opinion. Of those registered as Independents, 177 approved, 64 did not approve, and 801 had no opinion. Of the remaining respondents, who were not registered, 142 approved, 38 did not approve, and 44 had no opinion. Represent these data in a 3×4 matrix.

Consider the original budget matrix. Assume there is a 20% increase in manufacturing, a 4% increase in office, a 6% increase in sales, a 21% increase in shipping, a 5% increase in accounting, and a 4% decrease in management. Find the new budget matrix by developing a matrix A to represent these departmental increases and then computing the matrix BA. Mfg. = Manufacturing; Shp = Shipping; Act. = Accounting; Mgt. = Management ​ ​ ​

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

Evaluate the determinant. ​ ​

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