Question 1

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 2

Multiply the matrices. ​   ​

Accepted Answer

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

Question 3

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 4

An economy has an agricultural industry and a textile industry. Each unit of agricultural output requires 0.4 unit of agricultural input and 0.1 unit of textiles input. Each unit of textiles output requires 0.1 unit of agricultural input and 0.2 unit of textiles input. If surpluses of 5 units of agricultural products and 195 units of textiles are desired, find the gross production of each industry. ​

Accepted Answer

A)  agriculture = 60, textiles = 240 
B)  agriculture = 50, textiles = 250 
C)  agriculture = 60, textiles = 250 
D)  agriculture = 300, textiles = 250 
E)  agriculture = 60, textiles = 300 
A)  agriculture = 60, textiles = 240 
B)  agriculture = 50, textiles = 250 
C)  agriculture = 60, textiles = 250 
D)  agriculture = 300, textiles = 250 
E)  agriculture = 60, textiles = 300

Question 5

​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 U.S. trade balance with each country grouping in each year by finding matrix B - A. ​

Accepted Answer

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

Question 6

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.

Accepted Answer

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

Question 7

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) ​   ​
How many units of fuels were required to produce 1,000 units of power (utilities' goods)?
​

Accepted Answer

A)  0.5 
B)  5 
C)  54 
D)  5.4 
E)  59.9 
A)  0.5 
B)  5 
C)  54 
D)  5.4 
E)  59.9

Question 8

Solve for x, y and z. ​   ​

Accepted Answer

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

Question 9

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​
 
Let matrix A represent the matrix with the following elements:   .
Let matrix B represent the matrix with the following elements:   .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
​

Accepted Answer

A)  ​player 3 
B)  ​player 2 
C)  ​player 5 
D)  ​player 1 
E)  ​player 4 
A)  ​player 3 
B)  ​player 2 
C)  ​player 5 
D)  ​player 1 
E)  ​player 4

Question 10

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 11

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

Accepted Answer

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

Question 12

Card tables are made by joining 4 legs and a top using 4 bolts. The legs are each made from a steel rod. The top has a frame made from 4 steel rods. A cover and four special clamps that brace the top and hold the legs are joined to the frame using a total of 8 bolts. The parts-listing matrix for the card table assembly is given by ​   ​
If an order is received for 10 card tables, 4 legs, 1 top, 2 covers, 6 clamps, and 13 bolts, how many of each primary assembly item are required to fill the order?
​

Accepted Answer

A)  88 rods, 11 covers, 50 clamps, 141 bolts 
B)  88 rods, 88 covers, 141 clamps, 141 bolts 
C)  50 rods, 141 covers, 50 clamps, 141 bolts 
D)  88 rods, 13 covers, 50 clamps, 141 bolts 
E)  141 rods, 13 covers, 88 clamps, 88 bolts 
A)  88 rods, 11 covers, 50 clamps, 141 bolts 
B)  88 rods, 88 covers, 141 clamps, 141 bolts 
C)  50 rods, 141 covers, 50 clamps, 141 bolts 
D)  88 rods, 13 covers, 50 clamps, 141 bolts 
E)  141 rods, 13 covers, 88 clamps, 88 bolts

Question 13

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 4 
B)  Number 3 
C)  Number 8 
D)  Number 5 
E)  Number 1 
A)  Number 4 
B)  Number 3 
C)  Number 8 
D)  Number 5 
E)  Number 1

Question 14

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) ​   ​
Which industry is most dependent on its own goods for its operations?
​

Accepted Answer

A)  raw materials 
B)  agriculture and food 
C)  service 
D)  utilities 
E)  fuels 
A)  raw materials 
B)  agriculture and food 
C)  service 
D)  utilities 
E)  fuels

Question 15

What is element   ? ​   ​

Accepted Answer

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

Question 16

Evaluate the determinant. ​   ​

Accepted Answer

A)  31 
B)  1 
C)  8 
D)  23 
E)  10 
A)  31 
B)  1 
C)  8 
D)  23 
E)  10

Question 17

Multiplication by a matrix can be used to encode messages (and multiplication by its inverse can be used to decode messages). Given the code a b c d  
And the code matrix   , use matrix A to encode the message "To be or not to be."
​​

Accepted Answer

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

Question 18

A man has   invested in three properties. One earns 12%, one 10%, and one 8%. His annual income from the properties is   and the amount invested at 8% is twice that invested at 12%. What is the annual income from each property? ​

Accepted Answer

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

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 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? ​

Accepted Answer

A)  $220,000 at 7%, $0 at 8%, $0 at 10% 
B)  $180,000 at 7%, $10,000 at 8%, $30,000 at 10% 
C)  $190,000 at 7%, $0 at 8%, $30,000 at 10% 
D)  $30,000 at 7%, $0 at 8%, $190,000 at 10% 
E)  $190,000 at 7%, $20,000 at 8%, $10,000 at 10% 
A)  $220,000 at 7%, $0 at 8%, $0 at 10% 
B)  $180,000 at 7%, $10,000 at 8%, $30,000 at 10% 
C)  $190,000 at 7%, $0 at 8%, $30,000 at 10% 
D)  $30,000 at 7%, $0 at 8%, $190,000 at 10% 
E)  $190,000 at 7%, $20,000 at 8%, $10,000 at 10%

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

Multiply the matrices.

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. , ,

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.

Solve for x, y and z.

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

Use the matrices to find DE, if possible.

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?

What is element ?

Evaluate the determinant.

Multiplication by a matrix can be used to encode messages (and multiplication by its inverse can be used to decode messages). Given the code a b c d And the code matrix , use matrix A to encode the message "To be or not to be."

A man has invested in three properties. One earns 12%, one 10%, and one 8%. His annual income from the properties is and the amount invested at 8% is twice that invested at 12%. What is the annual income from each property?

Find the inverse matrix, if one exists.

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

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

Multiply the matrices. ​ ​

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. ​ , ,

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.

Solve for x, y and z. ​ ​

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

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

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? ​ ​

What is element ? ​ ​

Evaluate the determinant. ​ ​

Multiplication by a matrix can be used to encode messages (and multiplication by its inverse can be used to decode messages). Given the code a b c d And the code matrix , use matrix A to encode the message "To be or not to be." ​​

A man has invested in three properties. One earns 12%, one 10%, and one 8%. His annual income from the properties is and the amount invested at 8% is twice that invested at 12%. What is the annual income from each property? ​

Find the inverse matrix, if one exists.

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

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

Multiply the matrices.

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. , ,

Solve for x, y and z.

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

Use the matrices to find DE, if possible.

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?

What is element ?

Evaluate the determinant.

Multiplication by a matrix can be used to encode messages (and multiplication by its inverse can be used to decode messages). Given the code a b c d And the code matrix , use matrix A to encode the message "To be or not to be."

A man has invested in three properties. One earns 12%, one 10%, and one 8%. His annual income from the properties is and the amount invested at 8% is twice that invested at 12%. What is the annual income from each property?