Question 1

If possible, find   .   ,

Accepted Answer

A)     
B)    
C)     
D)     
E)  not possible 
A)     
B)    
C)     
D)     
E)  not possible A

Question 2

Find   .   ,

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)     D

Question 3

Which of the following is a product of elementary matrices for the matrix

Accepted Answer

A)    
B)    
C)     
D)    
E)     
A)    
B)    
C)     
D)    
E)     C

Question 4

Accepted Answer

A)  -1 
B)  0 
C)     
D)     
A)  -1 
B)  0 
C)     
D)

Question 5

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

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 6

Use inverse matrices and the graphing calculator to find the solution of the system of equations.

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 7

A system composed of two industries, coal and steel, has the inputs as seen below.(a) To produce 1 dollar's worth of output, the coal industry requires $0.30 of its own product and $0.70 of steel. (b) To produce 1 dollar's worth of output, the steel industry requires $0.30 of its own product and $0.10 of coal. Find D, the input-output matrix for this system. Then solve for the output matrix X in the equation   where the external demand is   . Round all the entries of the matrix to two decimal places, where applicable.

Accepted Answer

A)    
B)     
C)     
D)     
E)     
A)    
B)     
C)     
D)     
E)

Question 8

Find the inverse of the elementary matrix

Accepted Answer

A)     
B)     
C)    
D)     
E)     
A)     
B)     
C)    
D)     
E)

Question 9

A small community includes a farmer, a baker, and a grocer and has the input-output matrix   
and external demand matrix   . Solve for the output matrix X in the equation   .

Accepted Answer

A)     
B)    
C)     
D)     
E)     
A)     
B)    
C)     
D)     
E)

Question 10

Let   ,   . Find an elementary matrix E such that   .

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 11

A population of 10,000 is grouped as follows: 5,000 nonsmokers, 3,500 smokers of one pack or less per day, and 1,500 smokers of more than one pack per day. During any month there is a 5% probability that a nonsmoker will begin smoking a pack or less per day, and a 4% probability that a nonsmoker will begin smoking more than a pack per day. For smokers who smoke a pack or less per day, there is a 10% probability of quitting and a 10% probability of increasing to more than a pack per day. For smokers who smoke more than a pack per day, there is a 5% probability of quitting and a 20% probability of dropping to a pack or less per day. How many people will be in each of the three groups in 1 month?

Accepted Answer

A)  The number of people in each group is as follows: 5,475 nonsmokers, 3,150 smokers of one pack or less per day, and 1,375 smokers of more than one pack per day. 
B)  The number of people in each group is as follows: 4,975 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day. 
C)  The number of people in each group is as follows: 5,475 nonsmokers, 3,350 smokers of one pack or less per day, and 1,175 mokers of more than one pack per day. 
D)  The number of people in each group is as follows: 4,975 nonsmokers, 3,150 smokers of one pack or less per day, and 1,875 mokers of more than one pack per day. 
E)  The number of people in each group is as follows: 4,775 nonsmokers, 1,875 smokers of one pack or less per day, and 3,350 smokers of more than one pack per day. 
A)  The number of people in each group is as follows: 5,475 nonsmokers, 3,150 smokers of one pack or less per day, and 1,375 smokers of more than one pack per day. 
B)  The number of people in each group is as follows: 4,975 nonsmokers, 3,350 smokers of one pack or less per day, and 1,675 smokers of more than one pack per day. 
C)  The number of people in each group is as follows: 5,475 nonsmokers, 3,350 smokers of one pack or less per day, and 1,175 mokers of more than one pack per day. 
D)  The number of people in each group is as follows: 4,975 nonsmokers, 3,150 smokers of one pack or less per day, and 1,875 mokers of more than one pack per day. 
E)  The number of people in each group is as follows: 4,775 nonsmokers, 1,875 smokers of one pack or less per day, and 3,350 smokers of more than one pack per day.

Question 12

Use the matrices below. Perform the indicated operation.
AB   ,

Accepted Answer

A)     
B)    
C)     
D)     
E)     
A)     
B)    
C)     
D)     
E)

Question 13

Suppose that the table shows the numbers y of motor vehicle registrations (in millions) in the United States for the years 2000 through 2004. Use the method of least squares to find the least squares regression line for the data. Let t represent the year, with corresponding to 2000. Round the coefficient and constant of the equation to two decimal places

Accepted Answer

A)     
B)    
C)     
D)    
E)     
A)     
B)    
C)     
D)    
E)

Question 14

The market research department at a manufacturing plant determines that 30% of the people who purchase the plant's product during any month will not purchase it the next month. On the other hand, 40% of the people who do not purchase the product during any month will purchase it the next month. In a population of 1000 people, 100 people purchased the product this month. How many will purchase the product next month?

Accepted Answer

A)  510 people 
B)  570 people 
C)  430 people 
D)  400 people 
E)  370 people 
A)  510 people 
B)  570 people 
C)  430 people 
D)  400 people 
E)  370 people

Question 15

If possible, find   .   ,

Accepted Answer

A)     
B)     
C)    
D)     
E)  not possible 
A)     
B)     
C)    
D)     
E)  not possible

Question 16

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

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 17

Given matrix   . Find A-1 the inverse matrix.

Accepted Answer

A)     
B)     
C)     
D)     
E)     
A)     
B)     
C)     
D)     
E)

Question 18

If   and   , are C and D inverse matrices

Accepted Answer

A) True 
 B)False

Question 19

Find   . (Note: A2 = AA.)

Accepted Answer

A)     
B)     
C)     
D)     
E)  not possible 
A)     
B)     
C)     
D)     
E)  not possible

Question 20

A population of 100,000 consumers is grouped as follows: 20,000 users of Brand A, 30,000 users of Brand B, and 50,000 who use neither brand. During any month a Brand A user has a 20% probability of switching to Brand B and a 10% probability of not using either brand. A Brand B user has a 15% probability of switching to Brand A and a 20% probability of not using either brand. A nonuser has a 20% probability of purchasing Brand A and a 25% probability of purchasing Brand B. How many people will be in each group in 1 month?

Accepted Answer

A)  The number of people in each group is as follows: 30,300 users of Brand A, 36,000 users of Brand B, and 33,700 who use neither brand. 
B)  The number of people in each group is as follows: 41,700 users of Brand A, 28,500 users of Brand B, and 29,800 who use neither brand. 
C)  The number of people in each group is as follows: 35,500 users of Brand A, 30,300 users of Brand B, and 34,200 who use neither brand.? 
D)  The number of people in each group is as follows: 28,500 users of Brand A, 36,000 users of Brand B, and 35,500 who use neither brand. 
E)  The number of people in each group is as follows: 30,300 users of Brand A, 41,700 users of Brand B, and 28,000 who use neither brand. 
A)  The number of people in each group is as follows: 30,300 users of Brand A, 36,000 users of Brand B, and 33,700 who use neither brand. 
B)  The number of people in each group is as follows: 41,700 users of Brand A, 28,500 users of Brand B, and 29,800 who use neither brand. 
C)  The number of people in each group is as follows: 35,500 users of Brand A, 30,300 users of Brand B, and 34,200 who use neither brand.? 
D)  The number of people in each group is as follows: 28,500 users of Brand A, 36,000 users of Brand B, and 35,500 who use neither brand. 
E)  The number of people in each group is as follows: 30,300 users of Brand A, 41,700 users of Brand B, and 28,000 who use neither brand.

If possible, find . ,

Find . ,

Which of the following is a product of elementary matrices for the matrix

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

Use inverse matrices and the graphing calculator to find the solution of the system of equations.

Find the inverse of the elementary matrix

A small community includes a farmer, a baker, and a grocer and has the input-output matrix and external demand matrix . Solve for the output matrix X in the equation .

Let , . Find an elementary matrix E such that .

Use the matrices below. Perform the indicated operation. AB ,

If possible, find . ,

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

Given matrix . Find A^-1 the inverse matrix.

If and , are C and D inverse matrices

Find . (Note: A² = AA.)

Linear Equations

Determinants

Vector Spaces

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Exam 2: Matrices

If possible, find . ,

Find . ,

Which of the following is a product of elementary matrices for the matrix

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

Use inverse matrices and the graphing calculator to find the solution of the system of equations.

Find the inverse of the elementary matrix

A small community includes a farmer, a baker, and a grocer and has the input-output matrix and external demand matrix . Solve for the output matrix X in the equation .

Let , . Find an elementary matrix E such that .

Use the matrices below. Perform the indicated operation. AB ,

If possible, find . ,

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

Given matrix . Find A-1 the inverse matrix.

If and , are C and D inverse matrices

Find . (Note: A2 = AA.)

Linear Equations

Determinants

Vector Spaces

Inner Product Spaces

Linear Transformations

Eigenvalues Eigenvectors

Filters

Given matrix . Find A^-1 the inverse matrix.

Find . (Note: A² = AA.)