Question 1

Use the following matrices to perform the indicated matrix operations, if possible. ​   ​   ;   ​

Accepted Answer

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

Question 2

​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. ​
1   2       5       3   4
​Construct matrix B with elements   .
​

Accepted Answer

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

Question 3

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 4

If   and   , does   ?

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 5

Set up the system of equations and then solve it by using inverse matrices. ​
Bee ancestry Because a female bee comes from a fertilized egg and a male bee comes from an unfertilized egg, the number   of ancestors of a male t + 2 bee generations before the present generation is the sum of the number of ancestors t and t + 1 generations   before the present. If the numbers of ancestors of a male bee in a given generation t and in the previous generation are given by   , then there is a matrix M such that the numbers of ancestors in the two generations preceding generation t are given by   .
​
For a given male bee, the numbers of ancestors 5 and 6 generations back are given by   .
​
Find the numbers of ancestors 4 and 5 generations back by multiplying both sides of   by the inverse of M.
​

Accepted Answer

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

Question 6

We have encoded messages by assigning the letters of the alphabet the numbers 1-26, with a blank assigned the number 27, and by using an encoding matrix A that converts the numbers to the coded message. To decode any message encoded by A, we must find the inverse of A, denoted by A-1, and multiply A-1 times the coded message. Use this code and the given encoding matrix A to find the matrix that can be used to decode the given message. ​
Code matrix is
​   The message is
​
138, 59, 72, 29, 143, 58, 57, 24, 101, 44
​

Accepted Answer

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

Question 7

The following technology matrix describes the relationship of certain industries within the economy to each other. (A&F, agriculture and food; RM, raw materials; M, manufacturing; F, fuels industry; U, utilities; SI, service industries) ​   ​
For each 1,000 units of raw materials produced, how many units of service were required?
​

Accepted Answer

A) 14.4 
B) 144 
C) 9 
D) 0.9 
E) 159.3 
A) 14.4 
B) 144 
C) 9 
D) 0.9 
E) 159.3

Use the following matrices to perform the indicated matrix operations, if possible. ;

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. 1 2 5 3 4 Construct matrix B with elements .

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

If and , does ?

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

Use the following matrices to perform the indicated matrix operations, if possible. ​ ​ ; ​

​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. ​ 1 2 5 3 4 ​Construct matrix B with elements . ​

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

If and , does ?

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

Use the following matrices to perform the indicated matrix operations, if possible. ;

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. 1 2 5 3 4 Construct matrix B with elements .

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