Question 1

Write the word or phrase that best completes each statement or answers the question.
-

Accepted Answer

A)  (4, 1) 
B)  (4, -1) 
C)  (-4, -1) 
D)  (-4, 1)

Question 2

Provide an appropriate response.
-Only one of the following augmented matrices of a linear system is in a reduced form. Choose the matrix that is in reduced form.

Accepted Answer

A)   
B)   
C)   
D)

Question 3

Provide an appropriate response.
-Determine the value of each variable.

Accepted Answer

A)   
B)   
C)   
D)

Question 4

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and
 addition are possible and that inverses exist when needed.
-Solve for Y: XY + ZY = A

Accepted Answer

A)   
B)   
C)   
D)

Question 5

Provide an appropriate response.
-Given matrices M =  solve the matrix equations
MX = A and MX = B.

Accepted Answer

The answer of Provide an appropriate response.
-Given matrices M =...

Question 6

Write the word or phrase that best completes each statement or answers the question.
-

Accepted Answer

A)  (0, 8) 
B)  (-8, 0) 
C)  (0, -8) 
D)  (8, 0)

Question 7

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
-Labor and material costs for manufacturing each of three types of products M, N, and P are given in the table:
Product  The weekly allocation for labor is $50,000 and for materials is $80,000. There are to be 3 times as many units of product
M manufactured as units of product P. How many of each type of product would be manufactured each week to use
exactly each of the weekly allocations? Set up a system of linear equations, letting x1, x2, and x3 be the number
of units of products M, N, and P, respectively, manufactured in one week.

Accepted Answer

The answer of Find the system of equations to model...

Question 8

Perform the indicated row operations on the following matrix. 
-

Accepted Answer

A)   
B)   
C)   
D)

Question 9

Perform the operation, if possible.
-If a and b are nonzero real numbers and A =

Accepted Answer

The answer of Perform the operation, if possible.
-If a and...

Question 10

Solve the problem.
-Daisy has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $4.35, how many of the coins are nickels?

Accepted Answer

A)  9 nickels 
B)  21 nickels 
C)  7 nickels 
D)  16 nickels

Question 11

Perform the operation, if possible.
-A =  , B , B =  Find AB.

Accepted Answer

A)   
B)   
C)   
D)

Question 12

Solve the problem.
-A supermarket chain sells oranges, apples, peaches, and bananas in three stores located throughout a large
metropolitan area. The average number of pounds sold per day in each store is summarized in matrix M. "In
season" and "out of season" prices, per pound, of each fruit are given in matrix N. What is the total, for the three
stores, of "in season" daily revenue for the four fruits? The "out of season" peach sales represent what percentage of
the daily total "out of season" revenues for store 3?

Accepted Answer

The answer of Solve the problem.
-A supermarket chain sells oranges,...

Question 13

Solve the problem.
-Two sectors of a textbook economy are (1) communication equipment and (2) components and accessories. In 2005 the input-output table involving these two sectors was as follows.  Determine the production levels necessary in these two sectors to meet a demand for $80,000 of equipment and $90,000
Of components. Round to significant digits.

Accepted Answer

A)   
B)   
C)   
D)

Question 14

Solve the system as matrix equations using inverses.
-There were 340 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $490. How many adults and how many children attended?

Accepted Answer

A)  150 adults and 190 children 
B)  95 adults and 245 children 
C)  122 adults and 218 children 
D)  190 adults and 150 children

Question 15

Solve the problem.
-A large oil company produces three grades of gasoline: regular, unleaded, and super-unleaded. To produce
these gasolines, equipment is used which requires as input certain amounts of each of the three grades of
gasoline. To produce a dollar's worth of regular requires inputs of $0.14 worth of regular, $0.18 worth of
unleaded, and $0.17 worth of super-unleaded. To produce a dollar's worth of unleaded requires inputs of $0.14
worth of regular, $0.15 worth of unleaded, and $0.13 worth of super-unleaded. To produce a dollar's worth of
super-unleaded requires inputs of $0.15 worth of regular, $0.17 worth of unleaded, and $0.11 worth of
super-unleaded. In addition, the oil company has final demands for each of the different grades of gasoline.
Find the technology matrix that would be used in determining the total output of each grade of gasoline.

Accepted Answer

The answer of Solve the problem.
-A large oil company produces...

Question 16

Provide an appropriate response.
-Write the augmented matrix for the system.

Accepted Answer

A)   
B)   
C)   
D)

Question 17

Write the matrix equation as a system of linear equations without matrices.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 18

Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations.
-

Accepted Answer

A)   
B)   
C)   
D)

Question 19

Solve the problem.
-A chain of amusement parks pays experienced workers $240 per week and inexperienced workers $220 per week. The
total number of workers and total weekly wages at three different parks are given in the table. How many experienced
workers does each park employ? Set up a system of linear equations and solve using matrix inverse methods.

Accepted Answer

The answer of Solve the problem.
-A chain of amusement parks...

Question 20

Find the inverse, if it exists, of the given matrix.
-A =

Accepted Answer

A)   
B)   
C)  Does not exist 
D)

Exam 4: Graphing and Optimization

Write the word or phrase that best completes each statement or answers the question. -

Provide an appropriate response. -Only one of the following augmented matrices of a linear system is in a reduced form. Choose the matrix that is in reduced form.

Provide an appropriate response. -Determine the value of each variable.

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed. -Solve for Y: XY + ZY = A

Provide an appropriate response. -Given matrices M = solve the matrix equations MX = A and MX = B.

Write the word or phrase that best completes each statement or answers the question. -

Perform the indicated row operations on the following matrix. -

Perform the operation, if possible. -If a and b are nonzero real numbers and A =

Solve the problem. -Daisy has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $4.35, how many of the coins are nickels?

Perform the operation, if possible. -A = , B , B = Find AB.

Solve the system as matrix equations using inverses. -There were 340 people at a play. The admission price was $2 for adults and $1 for children. The admission receipts were $490. How many adults and how many children attended?

Provide an appropriate response. -Write the augmented matrix for the system.

Write the matrix equation as a system of linear equations without matrices. -

Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations. -

Find the inverse, if it exists, of the given matrix. -A =