Question 1

Find x, y, z and w. ​   ​

Accepted Answer

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

Question 2

A closed model for an economy has a manufacturing industry, utilities industry, and households industry. Each unit of manufacturing output uses 0.5 unit of manufacturing input, 0.4 unit of utilities input, and 0.1 unit of households input. Each unit of utilities output requires 0.4 unit of manufacturing input, 0.5 unit of utilities input, and 0.1 unit of households input. Each unit of household output requires 0.4 unit each of manufacturing and utilities input and 0.2 unit of households input. Find the gross production for each industry. ​

Accepted Answer

A) manufacturing = 6 households, utilities = 7 households 
B) manufacturing = households, utilities = households 
C) manufacturing = 2 households, utilities = 2 households 
D) manufacturing = 3 households, utilities = 3 households 
E) manufacturing = 4 households, utilities = 4 households 
A) manufacturing = 6 households, utilities = 7 households 
B) manufacturing = households, utilities = households 
C) manufacturing = 2 households, utilities = 2 households 
D) manufacturing = 3 households, utilities = 3 households 
E) manufacturing = 4 households, utilities = 4 households

Question 3

Use technology to solve the system of equations, if a solution exists.

Accepted Answer

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

Question 4

Find AB and BA if   and   , with   . ​

Accepted Answer

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

Question 5

Use the inverse to solve. ​   ​

Accepted Answer

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

Question 6

CD = DC. ​

Accepted Answer

A) True 
B) False 
A) True 
B) False

Question 7

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 8

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 9

Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries. ​   ​

Accepted Answer

A) government =  
Households, industry =  
Households 
B) government =  
Households, industry =  
Households 
C) government =  
Households, industry =  
Households 
D) government =  
Households, industry =  
Households 
E) government =  
Households, industry =  
Households 
A) government =  
Households, industry =  
Households 
B) government =  
Households, industry =  
Households 
C) government =  
Households, industry =  
Households 
D) government =  
Households, industry =  
Households 
E) government =  
Households, industry =  
Households

Question 10

The King Trucking Company has an order for three products for delivery. The following table gives the particulars for the products. ​   ​
If the carrier can carry 6,000 cu ft, can carry   , and is insured for   , how many units of each type can be carried?
​
​

Accepted Answer

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

Question 11

Use a graphing calculator to find the inverse of   . ​

Accepted Answer

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

Question 12

Use technology to find the determinant. ​   ​

Accepted Answer

A) 9 
B) 45 
C) 25 
D) 27 
E) 15 
A) 9 
B) 45 
C) 25 
D) 27 
E) 15

Question 13

Use determinants to decide whether the matrix has an inverse. ​

Accepted Answer

A) True 
B) False 
A) True 
B) False

Question 14

If the code matrix is   , find the matrix that can be used to decode the message 47, 36, 35, 28, 92, 69, 63, 93, 74, 56, 71, 57, 17, 17, 16. (Because A and A-1 are 3 × 3 matrices, use triples of numbers.) ​

Accepted Answer

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

Question 15

The inverse of matrix A is given. Use the inverse to solve for X. ​   Solve   .
​

Accepted Answer

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

Question 16

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 17

An irrigation system allows water to flow in the pattern shown in the figure below. Water flows into the system at A and exits at B, C, D, and E with the amounts shown. Using the fact that at each point the water entering equals the water leaving, formulate an equation for water flow at each of the five points and solve the system. ​   ​

Accepted Answer

A)   
,  
,  
,  
,  
(in thousands of gallons) 
B)   
,  
,  
,  
,  
(in thousands of gallons) 
C)   
,  
,  
,  
(in thousands of gallons) 
D)   
,  
,  
,  
,  
(in thousands of gallons) 
E)   
,  
,  
,  
,  
,  
(in thousands of gallons) 
A)   
,  
,  
,  
,  
(in thousands of gallons) 
B)   
,  
,  
,  
,  
(in thousands of gallons) 
C)   
,  
,  
,  
(in thousands of gallons) 
D)   
,  
,  
,  
,  
(in thousands of gallons) 
E)   
,  
,  
,  
,  
,  
(in thousands of gallons)

Question 18

Write the augmented matrix associated with the system.

Accepted Answer

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

Question 19

Use row operations on the augmented matrix to solve the given system of linear equations. ​   ​
​

Accepted Answer

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

Question 20

A brokerage house offers three stock portfolios. Portfolio I consists of 2 blocks of common stock and 1 municipal bond. Portfolio II consists of 4 blocks of common stock, 2 municipal bonds, and 3 blocks of preferred stock. Portfolio III consists of 7 blocks of common stock, 3 municipal bonds, and 3 blocks of preferred stock. A customer wants   blocks of common stock,   municipal bonds, and   blocks of preferred stock. How many units of each portfolio should be offered? ​

Accepted Answer

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

Find x, y, z and w.

Use technology to solve the system of equations, if a solution exists.

Find AB and BA if and , with .

Use the inverse to solve.

CD = DC.

Solve for x, y and z.

Find the inverse matrix, if one exists.

Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries.

The King Trucking Company has an order for three products for delivery. The following table gives the particulars for the products. If the carrier can carry 6,000 cu ft, can carry , and is insured for , how many units of each type can be carried?

Use a graphing calculator to find the inverse of .

Use technology to find the determinant.

Use determinants to decide whether the matrix has an inverse.

If the code matrix is , find the matrix that can be used to decode the message 47, 36, 35, 28, 92, 69, 63, 93, 74, 56, 71, 57, 17, 17, 16. (Because A and A^-1 are 3 × 3 matrices, use triples of numbers.)

The inverse of matrix A is given. Use the inverse to solve for X. Solve .

Find the inverse matrix, if one exists.

Write the augmented matrix associated with the system.

Use row operations on the augmented matrix to solve the given system of linear equations.

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 4: Matrices

Find x, y, z and w. ​ ​

Use technology to solve the system of equations, if a solution exists.

Find AB and BA if and , with . ​

Use the inverse to solve. ​ ​

CD = DC. ​

Solve for x, y and z. ​ ​

Find the inverse matrix, if one exists.

Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries. ​ ​

The King Trucking Company has an order for three products for delivery. The following table gives the particulars for the products. ​ ​ If the carrier can carry 6,000 cu ft, can carry , and is insured for , how many units of each type can be carried? ​ ​

Use a graphing calculator to find the inverse of . ​

Use technology to find the determinant. ​ ​

Use determinants to decide whether the matrix has an inverse. ​

If the code matrix is , find the matrix that can be used to decode the message 47, 36, 35, 28, 92, 69, 63, 93, 74, 56, 71, 57, 17, 17, 16. (Because A and A-1 are 3 × 3 matrices, use triples of numbers.) ​

The inverse of matrix A is given. Use the inverse to solve for X. ​ Solve . ​

Find the inverse matrix, if one exists.

Write the augmented matrix associated with the system.

Use row operations on the augmented matrix to solve the given system of linear equations. ​ ​ ​

Algebraic Concepts

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; Data Description

Derivatives

Applications of Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Find x, y, z and w.

Find AB and BA if and , with .

Use the inverse to solve.

CD = DC.

Solve for x, y and z.

Suppose the technology matrix for a closed model of a simple economy is given by matrix A. Find the gross productions for the industries.

The King Trucking Company has an order for three products for delivery. The following table gives the particulars for the products. If the carrier can carry 6,000 cu ft, can carry , and is insured for , how many units of each type can be carried?

Use a graphing calculator to find the inverse of .

Use technology to find the determinant.

Use determinants to decide whether the matrix has an inverse.

If the code matrix is , find the matrix that can be used to decode the message 47, 36, 35, 28, 92, 69, 63, 93, 74, 56, 71, 57, 17, 17, 16. (Because A and A^-1 are 3 × 3 matrices, use triples of numbers.)

The inverse of matrix A is given. Use the inverse to solve for X. Solve .

Use row operations on the augmented matrix to solve the given system of linear equations.