Question 1

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 2

In the analysis of traffic flow, a certain city estimates the following situation for the "square" of its downtown district. In the following figure, the arrows indicate the flow of traffic. If x1 represents the number of cars traveling between intersections A and B, x2 represents the number of cars traveling between B and C, x3 the number between C and D, and x4 the number between D and A, we can formulate equations based on the principle that the number of vehicles entering an intersection equals the number leaving it. That is, for intersection A we obtain   ​ Formulate equations for the traffic at B, C, and D. Solve the system of these four equations.
​   ​

Accepted Answer

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

Question 3

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations? ​

Accepted Answer

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

Question 4

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 5

Use inverse matrices to find the solution of the system of equations. ​   ​

Accepted Answer

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

Question 6

A botanist can purchase plant food of four different types, I, II, III, and IV. Each food comes in the same size bag, and the following table summarizes the number of grams of each of three nutrients that each bag contains. ​
 
The botanist wants to use a food that has these nutrients in a different proportion and determines that he will need a total of   of A,   of B, and   of C. Let x = Type I bags, y = Type II bags, z = Type III bags, and w = Type IV bags, where x, y, z, and w are non-negative amounts.
Find a general solution that will determine the number of bags of each type of food that should be ordered.
​
​

Accepted Answer

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

Question 7

If   and   , are C and D inverse matrices?

Accepted Answer

A) True 
 B)False

Question 8

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​

Accepted Answer

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

Question 9

One sector of an economy consists of a mining industry and a manufacturing industry, with technology matrix A. ​   ​
Surpluses of 32 units of mining output and 263 units of manufacturing output are desired. Find the gross production of each industry.
​

Accepted Answer

A)  mining = 790, manufacturing = 500 
B)  mining = 290, manufacturing = 500 
C)  mining = 285, manufacturing = 790 
D)  mining = 790, manufacturing = 495 
E)  mining = 290, manufacturing = 495 
A)  mining = 790, manufacturing = 500 
B)  mining = 290, manufacturing = 500 
C)  mining = 285, manufacturing = 790 
D)  mining = 790, manufacturing = 495 
E)  mining = 290, manufacturing = 495

Question 10

A log carrier has a body made from a 4-ft length of reinforced cloth having a patch on each side and a dowel slid through each end to act as handles. The parts-listing matrix for the log carrier is given by ​   ​
How many of each primary assembly items are required to fill an order for 500 log carriers and 30 handles?
​

Accepted Answer

A)  2060 handles, 970 cloths, 500 patches 
B)  1030 handles, 2060 cloths, 1000 patches 
C)  1030 handles, 500 cloths, 500 patches 
D)  1030 handles, 970 cloths, 2060 patches 
E)  1030 handles, 500 cloths, 2060 patches 
A)  2060 handles, 970 cloths, 500 patches 
B)  1030 handles, 2060 cloths, 1000 patches 
C)  1030 handles, 500 cloths, 500 patches 
D)  1030 handles, 970 cloths, 2060 patches 
E)  1030 handles, 500 cloths, 2060 patches

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

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations?

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

Use inverse matrices to find the solution of the system of equations.

If and , are C and D inverse matrices?

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.

One sector of an economy consists of a mining industry and a manufacturing industry, with technology matrix A. Surpluses of 32 units of mining output and 263 units of manufacturing output are desired. Find the gross production of each industry.

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 and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 3: Matrices

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

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations? ​

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

Use inverse matrices to find the solution of the system of equations. ​ ​

If and , are C and D inverse matrices?

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​

One sector of an economy consists of a mining industry and a manufacturing industry, with technology matrix A. ​ ​ Surpluses of 32 units of mining output and 263 units of manufacturing output are desired. Find the gross production of each industry. ​

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 and Data Description

Derivatives

Derivatives

Derivatives Continued

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

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

The following tables give the rank and number of registered dogs for the top ten breeds for 1995 and their 2002 data. Which breed had the largest increase in the number of registrations?

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

Use inverse matrices to find the solution of the system of equations.

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2.

One sector of an economy consists of a mining industry and a manufacturing industry, with technology matrix A. Surpluses of 32 units of mining output and 263 units of manufacturing output are desired. Find the gross production of each industry.