Question 1

Compute the indicated product. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)  the problem has no solution

Question 2

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

Accepted Answer

A)  ( 2, -10, -12 ) 
B)  ( 12, -10, -2 ) 
C)  ( -15, 12, 2 ) 
D)  ( 10, 12, -2 ) 
E)  ( 10, 12, 2 )

Question 3

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none.
​

Accepted Answer

The answer of Solve the system of linear equations using...

Question 4

Solve the linear system of equations. If the system is inconsistent, indicate this.

Accepted Answer

The answer of Solve the linear system of equations. If...

Question 5

An executive of Trident Communications recently traveled to London, Paris, and Rome. He paid $170, $230, and $150/night for lodging in London, Paris, and Rome, respectively, and his hotel bills totaled $4,240. He spent $110, $130, and $100/day for his meals in London, Paris, and Rome, respectively, and his expenses for meals totaled $2,670. If he spent as many days in London as he did in Paris and Rome combined, how many days did he stay in each city? ​

Accepted Answer

A)  14 days in London, 5 days in Paris, 9 days in Rome 
B)  12 days in London, 5 days in Paris, 7 days in Rome 
C)  16 days in London, 7 days in Paris, 9 days in Rome 
D)  7 days in London, 5 days in Paris, 12 days in Rome 
E)  14 days in London, 7 days in Paris, 7 days in Rome

Question 6

A university admissions committee anticipates an enrollment of 8,000 students in its freshman class next year. To satisfy admission quotas, incoming students have been categorized according to their sex and place of residence. The number of students in each category is given by the matrix  By using data accumulated in previous years, the admissions committee has determined that these students will elect to enter the College of Letters and Science, the College of Fine Arts, the School of Business Administration, and the School of Engineering according to the percentages that appear in the following matrix:  Find the matrix AB that shows the number of in-state, out-of-state, and foreign students expected to enter each discipline.

Accepted Answer

A)   
B)   
C)   
D)

Question 7

Compute the product. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 8

Find the inverse of the given matrix, if it exists. If not, write does not exist. Verify your answer.

Accepted Answer

The answer of Find the inverse of the given matrix,...

Question 9

Formulate but do not solve the problem.
​
The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $1.50/lb. If the blended coffee sells for $2.10/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)

Accepted Answer

The answer of Formulate but do not solve the problem.
​
The...

Question 10

Compute the product. ​  ​

Accepted Answer

A)   
B)   
C)   
D)

Question 11

Find the inverse of the matrix, if it exists. ​  ​

Accepted Answer

A)   
B)   
C)   
D)   
E)  the inverse does not exist

Question 12

Cantwell Associates, a real estate developer, is planning to build a new apartment complex consisting of one-bedroom units and two- and three-bedroom townhouses. A total of 192 units is planned, and the number of family units (two- and three-bedroom townhouses) will equal the number of one bedroom units. If the number of one-bedroom units will be 3 times the number of three-bedroom units, find how many units of each type will be in the complex. ​

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

A simple economy consists of three sectors: agriculture (A), manufacturing (M), and transportation (T). The input-output matrix for this economy is given by  If the units are measured in millions of dollars, determine the dollar amount of manufactured products required to produce $100 million worth of all goods in the economy.

Accepted Answer

A)  $60 million 
B)  $50 million 
C)  $80 million 
D)  $70 million

Question 14

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

Accepted Answer

The answer of Solve the system of linear equations using...

Question 15

A simple economy consists of two industries: agriculture and manufacturing. The production of 1 unit of agricultural products requires the consumption of 0.3 unit of agricultural products and 0.1 unit of manufactured goods. The production of 1 unit of manufactured products requires the consumption of 0.2 unit of agricultural products and 0.3 unit of manufactured goods. Round the answers to the nearest tenth.
​
Find the gross output of goods needed to satisfy a consumer demand for $120 million worth of agricultural products and $190 million worth of manufactured products.
​
$ __________ million
​
Find the value of the goods consumed in the internal process of production in order to meet the gross output.
​
$ __________ million

Accepted Answer

The answer of A simple economy consists of two industries:...

Question 16

Solve the linear system of equations. If the system is inconsistent, indicate this.
​

Accepted Answer

The answer of Solve the linear system of equations. If...

Question 17

A theater has a seating capacity of 450 and charges $2 for children, $3 for students, and $5 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $1,550. How many children attended the show? ​

Accepted Answer

A)  300 children 
B)  190 children 
C)  10 children 
D)  390 children 
E)  100 children

Question 18

Solve the linear system of equations ​  ​

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. If not, answer inconsistent.

Accepted Answer

The answer of Given that the augmented matrix in row-reduced...

Exam 2: Systems of Linear Equations and Matrices

Compute the indicated product. ​ ​

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

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none. ​

Solve the linear system of equations. If the system is inconsistent, indicate this.

Compute the product. ​ ​

Find the inverse of the given matrix, if it exists. If not, write does not exist. Verify your answer.

Compute the product. ​ ​

Find the inverse of the matrix, if it exists. ​ ​

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

Solve the linear system of equations. If the system is inconsistent, indicate this. ​

A theater has a seating capacity of 450 and charges $2 for children, $3 for students, and $5 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $1,550. How many children attended the show? ​

Solve the linear system of equations ​ ​

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

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. If not, answer inconsistent.

Compute the indicated product.

Solve the system of linear equations using the Gauss-Jordan elimination method. If there is no solution, answer none.

Compute the product.

Compute the product.

Find the inverse of the matrix, if it exists.

Solve the linear system of equations. If the system is inconsistent, indicate this.

A theater has a seating capacity of 450 and charges $2 for children, $3 for students, and $5 for adults. At a certain screening with full attendance, there were half as many adults as children and students combined. The receipts totaled $1,550. How many children attended the show?

Solve the linear system of equations

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