Question 1

Identify the row matrix. What is its transpose?

Accepted Answer

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

Question 2

Formulate but do not solve the problem. ​
The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $43 and $22/acre, respectively. Jacob Johnson has $17,300 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Let x be the number of acres allotted for cultivating corn.
​

Accepted Answer

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

Question 3

Find the transpose of the given matrix.

Accepted Answer

The answer of Find the transpose of the given matrix....

Question 4

Formulate but do not solve the problem. Kelly Fisher has a total of $31,000 invested in two municipal bonds that have yields of $0.07% and $0.05% interest per year, respectively. If the interest Kelly receives from the bonds in a year is $1,790, how much does she have invested in each bond? Let x the bond with $0.07% interest per year.

Accepted Answer

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

Question 5

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​  ...

Question 6

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​   ​

Accepted Answer

A)  $19.91 million, $21.48 million and $9.04 million output of the first, the second and the third sectors respectively 
B)  $27.91 million, $21.48 million and $2.04 million output of the first, the second and the third sectors respectively 
C)  $19.91 million, $25.48 million and $2.04 million output of the first, the second and the third sectors respectively 
D)  $27.91 million, $25.48 million and $9.04 million output of the first, the second and the third sectors respectively 
A)  $19.91 million, $21.48 million and $9.04 million output of the first, the second and the third sectors respectively 
B)  $27.91 million, $21.48 million and $2.04 million output of the first, the second and the third sectors respectively 
C)  $19.91 million, $25.48 million and $2.04 million output of the first, the second and the third sectors respectively 
D)  $27.91 million, $25.48 million and $9.04 million output of the first, the second and the third sectors respectively

Question 7

Formulate but do not solve the problem. ​
A private investment club has $600,000 earmarked for investment in stocks. To arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high-risk, medium-risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year; medium-risk stocks, 12%/year; and low risk stocks, 5%/year. The members have decides that the investment in medium-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $60,000/year on the total investment. (Assume that all the money available for investment is invested). Let x be the amount of money invested in high-risk stocks, y be the amount of money invested in medium-risk stocks, and z be the amount of money invested in low-risk stocks.
​

Accepted Answer

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

Question 8

Indicate whether the matrix is in row-reduced form. Answer yes or no.

Accepted Answer

The answer of Indicate whether the matrix is in row-reduced...

Question 9

Company TKK Corporation, a large conglomerate, has three subsidiaries engaged in producing raw rubber, manufacturing tires, and manufacturing other rubber-based goods. The production of 1 unit of raw rubber requires the consumption of 0.02 unit of rubber, 0.05 unit of tires, and 0.01 unit of other rubber-based goods. To produce 1 unit of tires requires 0.8 unit of raw rubber, 0.04 unit of tires, and 0 units of other rubber-based goods. To produce 1 unit of other rubber-based goods requires 0.3 unit of raw rubber, 0.02 unit of tires, and 0.07 unit of other rubber-based goods. Market research indicates that the demand for the following year will be $300 million for raw rubber, $500 million for tires, and $120 million for other rubber-based products. Suppose the demand for raw rubber increases by 10%, the demand for tires increases by 20%, and the demand for other rubber-based products decreases by 10%. Find the level of production for each subsidiary in order to satisfy this demand. Round the answers to the nearest tenth.
​
$ __________ million worth of raw rubber
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$ __________ million worth of tires
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$ __________ million worth of other rubber-based goods

Accepted Answer

The answer of Company TKK Corporation, a large conglomerate, has...

Question 10

The manegement of Hartman Rent-A-Car has allocated $1,512,000 to purchase 60 new automobiles to add to the existing fleet of rental cars. The company will choose from compact, mid-sized, and full sized cars costing $18,000, $28,800, and $39,600 each, respectively. find formulas giving the options available to the company. ​

Accepted Answer

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

Question 11

Solve the system of linear equations using the Gauss-Jordan elimination method.

Accepted Answer

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

Question 12

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​   ​

Accepted Answer

A)  $43.33 million and $34.67 million output of the first and the second sector respectively 
B)  $22.33 million and $34.67 million output of the first and the second sector respectively 
C)  $43.33 million and $46.67 million output of the first and the second sector respectively 
D)  $22.33 million and $46.67 million output of the first and the second sector respectively 
A)  $43.33 million and $34.67 million output of the first and the second sector respectively 
B)  $22.33 million and $34.67 million output of the first and the second sector respectively 
C)  $43.33 million and $46.67 million output of the first and the second sector respectively 
D)  $22.33 million and $46.67 million output of the first and the second sector respectively

Question 13

Determine the value of k for which the system of linear equations has no solution. ​   ​

Accepted Answer

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

Question 14

A theater has a seating capacity of 750 and charges $2 for children, $4 for students, and $5 for adults. At a certain screening with full attendance, there were one-fourth as many adults as children and students combined. The receipts totaled $2,150. How many children attended the show?
​
__________ children

Accepted Answer

The answer of A theater has a seating capacity of...

Question 15

Let       ​ Does   equal   ?
​

Accepted Answer

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

Question 16

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Accepted Answer

A)  x = 6, y = -16 
B)  x = 4, y = -19 
C)  x = 4, y = -16 
D)  x = 6, y = -19 
E)  The system is inconsistent. 
A)  x = 6, y = -16 
B)  x = 4, y = -19 
C)  x = 4, y = -16 
D)  x = 6, y = -19 
E)  The system is inconsistent.

Question 17

Solve the linear system of equations ​   ​

Accepted Answer

A)  Unique solution:   
B)  Unique solution:   
C)  Infinitely many solutions;   
D)  No solution 
A)  Unique solution:   
B)  Unique solution:   
C)  Infinitely many solutions;   
D)  No solution

Question 18

Find the inverse of the given matrix, if it exists. Verify your answer. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The inverse matrix does not exist. 
A)    
B)    
C)    
D)    
E)  The inverse matrix does not exist.

Question 19

Solve the system of linear equations using the Gauss-Jordan elimination method.

Accepted Answer

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

Question 20

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.4 unit of agricultural products and 0.3 unit of manufactured goods. The production of 1 unit of manufactured products requires the consumption of 0.2 unit of agricultural products and 0.4 unit of manufactured goods. ​
Find the gross output of goods needed to satisfy a consumer demand for $100 million worth of agricultural products and $100 million worth of manufactured products. Round answers to two decimal places.
​

Accepted Answer

A)  $275.31 million and $300.00 million worth of agricultural goods and manufactured products respectively 
B)  $275.31 million and $323.99 million worth of agricultural goods and manufactured products respectively 
C)  $266.67 million and $300.00 million worth of agricultural goods and manufactured products respectively 
D)  $266.67 million and $323.99 million worth of agricultural goods and manufactured products respectively 
A)  $275.31 million and $300.00 million worth of agricultural goods and manufactured products respectively 
B)  $275.31 million and $323.99 million worth of agricultural goods and manufactured products respectively 
C)  $266.67 million and $300.00 million worth of agricultural goods and manufactured products respectively 
D)  $266.67 million and $323.99 million worth of agricultural goods and manufactured products respectively

Identify the row matrix. What is its transpose?

Find the transpose of the given matrix.

Compute the product.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met.

Indicate whether the matrix is in row-reduced form. Answer yes or no.

Solve the system of linear equations using the Gauss-Jordan elimination method.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met.

Determine the value of k for which the system of linear equations has no solution.

Let Does equal ?

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Solve the linear system of equations

Find the inverse of the given matrix, if it exists. Verify your answer.

Solve the system of linear equations using the Gauss-Jordan elimination method.

Straight Lines and Linear Functions

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 2: Systems of Linear Equations and Matrices

Identify the row matrix. What is its transpose?

Find the transpose of the given matrix.

Compute the product. ​

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​ ​

Indicate whether the matrix is in row-reduced form. Answer yes or no.

Solve the system of linear equations using the Gauss-Jordan elimination method.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met. ​ ​

Determine the value of k for which the system of linear equations has no solution. ​ ​

Let ​ Does equal ? ​

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Solve the linear system of equations ​ ​

Find the inverse of the given matrix, if it exists. Verify your answer. ​ ​

Solve the system of linear equations using the Gauss-Jordan elimination method.

Straight Lines and Linear Functions

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Compute the product.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met.

Matrix A is an input-output matrix associated with an economy, and matrix D (units in millions of dollars) is a demand vector. Find the final outputs of each industry so that the demands of both industry and the open sector are met.

Determine the value of k for which the system of linear equations has no solution.

Let Does equal ?

Solve the linear system of equations

Find the inverse of the given matrix, if it exists. Verify your answer.