Exam 3: Matrices

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.

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.

Multiply the matrices. ​ ​

Write the augmented matrix associated with the system.

Use technology to find the determinant. ​ ​

The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; M, manufacturing; F, fuels industry; U, utilities; SI, service industries) ​ ​ For each 1,000 units of raw materials produced, how many units of service were required? ​

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

Multiply the matrices. ​

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) ​

A manufacturer of table saws has three models: Deluxe, Premium, and Ultimate, which must be painted, assembled, and packaged for shipping. The table gives the number of hours required for each of these operations for each type of table saw. If the manufacturer has 98 hours available per day for painting, 150 hours for assembly, and 36 hours for packaging, how many of each type of saw can be produced each day? ​ ​

Use technology to find the determinant. ​ ​

Suppose the weights (in grams) and lengths (in centimeters) of three groups of laboratory animals are given by matrix A, where column 1 gives the lengths and each row corresponds to one group. ​ ​ ​If the increase in both weight and length over the next two weeks is 19% for group I, 9% for group II, and 3% for group III, then the increases in the measures during the 2 weeks can be found by computing GA, where ​ What are the increases in respective weights and measures at the end of these 2 weeks? ​

Find the inverse matrix, if one exists.

Write the transpose of matrix F. ​ ​

Use the matrices below. Perform the indicated operations. ​ BA ​ ​ ​

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. ​

Find the inverse matrix, if one exists.

Write the matrix that is the negative of matrix B. ​ ​

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. ​​ ​

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