Question 1

Find x, y, z and w. ​   ​

Accepted Answer

A)   
, and   
B)   
, and   
C)   
, and   
D)   
, and   
E)   
, and   
A)   
, and   
B)   
, and   
C)   
, and   
D)   
, and   
E)   
, and

Question 2

In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If   represents the number of cars traveling between intersections A and B,   represents the number of cars traveling between B and C,   the number between C and D, and   the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain   Formulate equations for the traffic at B, C, and D. ​   ​

Accepted Answer

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

Question 3

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient? ​   ​

Accepted Answer

A) Number 1 
B) Number 4 
C) Number 3 
D) Number 8 
A) Number 1 
B) Number 4 
C) Number 3 
D) Number 8

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

A)   
,  
,  
, for any real number  
And  
) 
B)   
,  
,  
,  
,   
C)   
,  
,  
,  
,   
D)   
,  
,  
, for any real number  
And  
) 
E) no solution 
A)   
,  
,  
, for any real number  
And  
) 
B)   
,  
,  
,  
,   
C)   
,  
,  
,  
,   
D)   
,  
,  
, for any real number  
And  
) 
E) no solution

Question 6

Suppose the economy of an underdeveloped country has an agricultural industry and an oil industry, with technology matrix A. ​   ​
If surpluses of 0 units of agricultural products and 610 units of oil products are desired, find the gross production of each industry to the nearest unit.
​

Accepted Answer

A) agricultural = 800, oil = 825 
B) agricultural = 110, oil = 700 
C) agricultural = 110, oil = 715 
D) agricultural = 100, oil = 715 
E) agricultural = 100, oil = 700 
A) agricultural = 800, oil = 825 
B) agricultural = 110, oil = 700 
C) agricultural = 110, oil = 715 
D) agricultural = 100, oil = 715 
E) agricultural = 100, oil = 700

Question 7

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 8

Multiply the matrices.   ​

Accepted Answer

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

Question 9

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.

Accepted Answer

A)   
,  
, for any real number z. 
B)   
,  
,   
C)   
,  
, for any real number z. 
D)   
,  
, for any real number z. 
E) no solution 
A)   
,  
, for any real number z. 
B)   
,  
,   
C)   
,  
, for any real number z. 
D)   
,  
, for any real number z. 
E) no solution

Question 10

The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different. ​
United States   Foreign   ​

Accepted Answer

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

Question 11

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? ​     ​

Accepted Answer

A) They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
B) They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
C) They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days. 
D) They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
E) They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days. 
A) They paid 30% of the debts due in 30 days, 100% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
B) They paid 30% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
C) They paid 100% of the debts due in 30 days, 100% of the debts due in 60 days, and 30% of the debts due in more than 60 days. 
D) They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 100% of the debts due in more than 60 days. 
E) They paid 100% of the debts due in 30 days, 30% of the debts due in 60 days, and 30% of the debts due in more than 60 days.

Question 12

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.     ​

Accepted Answer

A)   
​,  
, for any real number z. 
B) ​  
,  
, for any real number z. 
C) ​  
,  
, for any real number z. 
D) ​  
,  
, for any real number z. 
E) ​no solution 
A)   
​,  
, for any real number z. 
B) ​  
,  
, for any real number z. 
C) ​  
,  
, for any real number z. 
D) ​  
,  
, for any real number z. 
E) ​no solution

Question 13

A log carrier has a body made from a 4-ft length of reinforced cloth having a patch on each side and a dowel slid through each end to act as handles. The parts-listing matrix for the log carrier is given by ​   ​
How many of each primary assembly items are required to fill an order for 500 log carriers and 30 handles?
​

Accepted Answer

A) 2060 handles, 970 cloths, 500 patches 
B) 1030 handles, 2060 cloths, 1000 patches 
C) 1030 handles, 500 cloths, 500 patches 
D) 1030 handles, 970 cloths, 2060 patches 
E) 1030 handles, 500 cloths, 2060 patches 
A) 2060 handles, 970 cloths, 500 patches 
B) 1030 handles, 2060 cloths, 1000 patches 
C) 1030 handles, 500 cloths, 500 patches 
D) 1030 handles, 970 cloths, 2060 patches 
E) 1030 handles, 500 cloths, 2060 patches

Question 14

Three different bacteria are cultured in one dish and feed on three nutrients. Each individual of species I consumes 1 unit of each of the first and second nutrients and 2 units of the third nutrient. Each individual of species II consumes 2 units of the first nutrient and 2 units of the third nutrient. Each individual of species III consumes 2 units of the first nutrient, 3 units of the second nutrient, and 5 units of the third nutrient. Let x1, x2 and x3 represent species I, II and III respectively. If the culture is given   units of the first nutrient,   units of the second nutrient, and   units of the third nutrient, how many of each species can be supported such that all of the nutrients are consumed? ​

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Find the inverse matrix, if one exists.

Accepted Answer

A)    
B)    
C)    
D)    
E) no inverse exists 
A)    
B)    
C)    
D)    
E) no inverse exists

Question 17

A bank lent   million for the development of three new products, with one loan at 6%, one loan at 7%, and the third loan at 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and the bank's annual income from the loans was   . How much was lent at each rate? ​

Accepted Answer

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

Question 18

For   , what size is each product FFT and FTF? ​​

Accepted Answer

A) FFT is 2×2; FTF is 2×2 
B) FFT is 2×2; FTF is 4×4 
C) FFT is 4×2; FTF is 4×4 
D) FFT is 4×4; FTF is 2×2 
E) FFT is 2×4; FTF is 4×2 
A) FFT is 2×2; FTF is 2×2 
B) FFT is 2×2; FTF is 4×4 
C) FFT is 4×2; FTF is 4×4 
D) FFT is 4×4; FTF is 2×2 
E) FFT is 2×4; FTF is 4×2

Question 19

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

Accepted Answer

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

Question 20

If matrix M has element   , what is   ? ​   ​

Accepted Answer

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

Find x, y, z and w.

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient?

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

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

Suppose the economy of an underdeveloped country has an agricultural industry and an oil industry, with technology matrix A. If surpluses of 0 units of agricultural products and 610 units of oil products are desired, find the gross production of each industry to the nearest unit.

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

Multiply the matrices.

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.

The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different. United States Foreign

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.

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

Find the inverse matrix, if one exists.

A bank lent million for the development of three new products, with one loan at 6%, one loan at 7%, and the third loan at 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and the bank's annual income from the loans was . How much was lent at each rate?

For , what size is each product FFT and F^TF?

Use the matrices below. Perform the indicated operations. BA

If matrix M has element , what is ?

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 4: Matrices

Find x, y, z and w. ​ ​

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient? ​ ​

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

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

Suppose the economy of an underdeveloped country has an agricultural industry and an oil industry, with technology matrix A. ​ ​ If surpluses of 0 units of agricultural products and 610 units of oil products are desired, find the gross production of each industry to the nearest unit. ​

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

Multiply the matrices. ​

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.

The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different. ​ United States Foreign ​

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. ​

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

Find the inverse matrix, if one exists.

A bank lent million for the development of three new products, with one loan at 6%, one loan at 7%, and the third loan at 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and the bank's annual income from the loans was . How much was lent at each rate? ​

For , what size is each product FFT and FTF? ​​

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

If matrix M has element , what is ? ​ ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Find x, y, z and w.

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient?

Suppose the economy of an underdeveloped country has an agricultural industry and an oil industry, with technology matrix A. If surpluses of 0 units of agricultural products and 610 units of oil products are desired, find the gross production of each industry to the nearest unit.

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

Multiply the matrices.

The tables below give the numbers of some species of threatened and endangered wildlife in the United States and in foreign countries in 2003. Find a matrix with the total number of these species. Assume that U.S. and foreign species are different. United States Foreign

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.

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

A bank lent million for the development of three new products, with one loan at 6%, one loan at 7%, and the third loan at 8%. The amount lent at 8% was equal to the sum of the amounts lent at the other two rates, and the bank's annual income from the loans was . How much was lent at each rate?

For , what size is each product FFT and F^TF?

Use the matrices below. Perform the indicated operations. BA

If matrix M has element , what is ?