Question 1

Solve for u, x, y, and z in the matrix equation.

Accepted Answer

A)      
B)      
C)      
D)      
E)

Question 2

Formulate but do not solve the problem. Cantwell Associates, a real estate devloper, is planning to build a new apartment complex consisting of one bedroom units and two- and three- bedroom townhouses. A total of  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  times the number of three-bedroom units, find how many units of each type will be in the complex. Let x be the number of one-bedroom units, y be the number of two-bedroom units, and z be the number of three-bedroom units.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 3

Perform the indicated operations.

Accepted Answer

A)   
B)   
C)   
D)

Question 4

Compute the indicated product. ​  ​

Accepted Answer

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

Question 5

Perform the indicated operations.

Accepted Answer

The answer of Perform the indicated operations. ...

Question 6

Writing the system of equations as a matrix equation solve the system of equations by using the inverse of the coefficient matrix.
​

Accepted Answer

The answer of Writing the system of equations as a...

Question 7

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.

Accepted Answer

A)   
B)   
C)   
D)   
E)  The system is inconsistent

Question 8

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.

Accepted Answer

A)   
B)   
C)   
D)   
E)  The system is inconsistent.

Question 9

Solve the matrix equation  for the matrices A and D.

Accepted Answer

The answer of Solve the matrix equation  for the...

Question 10

Determine the value of k so that the following system of linear equations has a solution and then find the solution.
​  ​  __________
​  __________
​  __________

Accepted Answer

The answer of Determine the value of k so that...

Question 11

William and Michael's stock holdings are given by the matrix  At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

Accepted Answer

The answer of William and Michael's stock holdings are given...

Question 12

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 13

Formulate but do not solve the problem. A theater has a seating capacity of 600 and charges $6 for children, $11 for students, and $16 for adults. At a certain screening with full attendance, there were half as many adult as children and students combined. The receipts totaled $1,800. How many children attended the show?
Let x be the number of tickets sold to children, y be the number of tickets sold to students, and z be the number of tickets sold to adults.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 14

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 15

The property damage claim frequencies per 100 cars in Massachusetts in the year 2000, 2001, 2002 were 6.87, 7.05, and 7.13, respectively. The corresponding claim frequencies in the United States were 4.1,  and 4.07 respectively. Express this information using a 2×3 matrix.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 16

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 0.3 unit of manufactured goods.
​
Find the gross output of goods if the consumer demand for the output of agricultural goods and the consumer demand for manufactured products are $120 million and $140 million, respectively. Round answers to two decimal places, if necessary.
​
$__________ million worth of agricultural goods
​
$__________ million worth of manufactured products.
​
Find the value of the goods consumed in the internal process of production in order to meet the gross output. Round answers to two decimal places, if necessary.
​
$__________ million worth of agricultural goods
​
$__________ million worth of manufactured products.

Accepted Answer

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

Question 17

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​  ...

Question 18

The accompanying figure shows the flow of traffic near a city's Civic Center during the rush hours on a typical weekday. Each road can handle a maximum of 1,000 cars/hour without causing congestion. The flow of traffic is controlled by traffic lights at each of the five intersections.  Set up a system of linear equations describing the traffic flow and solve this system.

Accepted Answer

A)   
B)   
C)   
D)   
E)  The system is inconsistent.

Question 19

Find the transpose of the given matrix.

Accepted Answer

A)   
B)   
C)   
D)

Question 20

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...

Exam 2: Systems of Linear Equations and Matrices

Solve for u, x, y, and z in the matrix equation.

Perform the indicated operations.

Compute the indicated product.

Perform the indicated operations.

Writing the system of equations as a matrix equation solve the system of equations by using the inverse of the coefficient matrix.

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.

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.

Solve the matrix equation for the matrices A and D.

Determine the value of k so that the following system of linear equations has a solution and then find the solution. __

William and Michael's stock holdings are given by the matrix At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

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

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

The property damage claim frequencies per 100 cars in Massachusetts in the year 2000, 2001, 2002 were 6.87, 7.05, and 7.13, respectively. The corresponding claim frequencies in the United States were 4.1, and 4.07 respectively. Express this information using a 2×3 matrix.

Compute the product.

Find the transpose of the given matrix.

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

Exam 2: Systems of Linear Equations and Matrices

Solve for u, x, y, and z in the matrix equation.

Perform the indicated operations.

Compute the indicated product. ​ ​

Perform the indicated operations.

Writing the system of equations as a matrix equation solve the system of equations by using the inverse of the coefficient matrix. ​

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.

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.

Solve the matrix equation for the matrices A and D.

Determine the value of k so that the following system of linear equations has a solution and then find the solution. ​ ​ __________ ​ __________ ​ __________

William and Michael's stock holdings are given by the matrix At the close of trading on a certain day, the prices (in dollars per share) of the stocks are given by the matrix

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

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

The property damage claim frequencies per 100 cars in Massachusetts in the year 2000, 2001, 2002 were 6.87, 7.05, and 7.13, respectively. The corresponding claim frequencies in the United States were 4.1, and 4.07 respectively. Express this information using a 2×3 matrix.

Compute the product. ​

Find the transpose of the given matrix.

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

Compute the indicated product.

Writing the system of equations as a matrix equation solve the system of equations by using the inverse of the coefficient matrix.

Determine the value of k so that the following system of linear equations has a solution and then find the solution. __

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

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

Compute the product.