Question 1

What is the sum of matrix M and its negative? ​   ​

Accepted Answer

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

Question 2

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 3

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)    ,   ,   
B)    ,   ,   
C)    ,   ,   
D)    ,   ,   
E)  no solution 
A)    ,   ,   
B)    ,   ,   
C)    ,   ,   
D)    ,   ,   
E)  no solution

Question 4

Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation.
​     ,   ,

Accepted Answer

A) True 
 B)False

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

Accepted Answer

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

Question 7

For   , are FFT and FTF defined?

Accepted Answer

A) True 
 B)False

Question 8

For the economy, what industry is most dependent on utilities? ​   ​

Accepted Answer

A)  Agriculture 
B)  Utilities 
C)  Manufacturing 
D)  Fules 
E)  All industries equally depend on utilities. 
A)  Agriculture 
B)  Utilities 
C)  Manufacturing 
D)  Fules 
E)  All industries equally depend on utilities.

Question 9

Write the augmented matrix associated with the system.

Accepted Answer

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

Question 10

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

Accepted Answer

A)    
B)    
C)    
D)    
E)    is undefined 
A)    
B)    
C)    
D)    
E)    is undefined

Question 11

Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A. ​   ​
If surpluses of 40 agricultural units and 70 mineral units are desired, find the gross production to the nearest unit for each industry.
​

Accepted Answer

A)  agriculture = 167, minerals = 103 
B)  agriculture = 65, minerals = 167 
C)  agriculture = 71, minerals = 96 
D)  agriculture = 71, minerals = 103 
E)  agriculture = 65, minerals = 96 
A)  agriculture = 167, minerals = 103 
B)  agriculture = 65, minerals = 167 
C)  agriculture = 71, minerals = 96 
D)  agriculture = 71, minerals = 103 
E)  agriculture = 65, minerals = 96

Question 12

Let matrix A represent the sales (in thousands of dollars) for the Walbash Company in 2004 in various cities, and let matrix B represent the sales (in thousands of dollars) for the same company in 2005 in the same cities. Write the matrix that represents the change in sales by type (wholesale and retail) and city (Chicago, Atlanta, and Memphis) from 2004 to 2005. ​   ​     ;   ​

Accepted Answer

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

Question 13

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) ​

Accepted Answer

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

Question 14

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 15

​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. Suppose Maxx Industries pays 20% of the amount owed on each loan. Write the matrix that would give the remaining debt in each category. ​

Accepted Answer

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

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

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

Accepted Answer

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

Question 18

Suppose that an economy can be represented by the technology matrix below. If surpluses of 180 units of fishing output, 93 units of agricultural goods, and 40 units of mining goods are desired, find the gross production to the nearest unit of each industry. ​   ​

Accepted Answer

A)  fishing = 632, agriculture = 796, mining = 570 
B)  fishing = 633, agriculture = 796, mining = 568 
C)  fishing = 632, agriculture = 796, mining = 568 
D)  fishing = 632, agriculture = 793, mining = 568 
E)  fishing = 633, agriculture = 793, mining = 570 
A)  fishing = 632, agriculture = 796, mining = 570 
B)  fishing = 633, agriculture = 796, mining = 568 
C)  fishing = 632, agriculture = 796, mining = 568 
D)  fishing = 632, agriculture = 793, mining = 568 
E)  fishing = 633, agriculture = 793, mining = 570

Question 19

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 20

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)

What is the sum of matrix M and its negative?

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.

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.

Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. , ,

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

Use the matrices below. Perform the indicated operations.

For , are FFT and F^TF defined?

For the economy, what industry is most dependent on utilities?

Write the augmented matrix associated with the system.

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

Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A. If surpluses of 40 agricultural units and 70 mineral units are desired, find the gross production to the nearest unit for each industry.

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

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

Use the matrices below. Perform the indicated operations. AZ

Suppose that an economy can be represented by the technology matrix below. If surpluses of 180 units of fishing output, 93 units of agricultural goods, and 40 units of mining goods are desired, find the gross production to the nearest unit of each industry.

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?

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 and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 3: Matrices

What is the sum of matrix M and its negative? ​ ​

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.

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.

Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. ​ , ,

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

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

For , are FFT and FTF defined?

For the economy, what industry is most dependent on utilities? ​ ​

Write the augmented matrix associated with the system.

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

Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A. ​ ​ If surpluses of 40 agricultural units and 70 mineral units are desired, find the gross production to the nearest unit for each industry. ​

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

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

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

Suppose that an economy can be represented by the technology matrix below. If surpluses of 180 units of fishing output, 93 units of agricultural goods, and 40 units of mining goods are desired, find the gross production to the nearest unit of each industry. ​ ​

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? ​

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 and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

What is the sum of matrix M and its negative?

Substitute the given values of x, y, and z into the matrix equation and use matrix multiplication to determine if the values satisfy the equation. , ,

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

Use the matrices below. Perform the indicated operations.

For , are FFT and F^TF defined?

For the economy, what industry is most dependent on utilities?

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

Suppose an economy has two industries, agriculture and minerals. Suppose further that the technology matrix for this economy is A. If surpluses of 40 agricultural units and 70 mineral units are desired, find the gross production to the nearest unit for each industry.

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

Use the matrices below. Perform the indicated operations. AZ

Suppose that an economy can be represented by the technology matrix below. If surpluses of 180 units of fishing output, 93 units of agricultural goods, and 40 units of mining goods are desired, find the gross production to the nearest unit of each industry.

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?