Question 1

Find the inverse of the matrix if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E) Does not exist 
A)    
B)    
C)    
D)    
E) Does not exist

Question 2

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 3

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 4

Use matrices to solve the system.

Accepted Answer

A)    
B)    
C)    
D) The equations are dependent 
E) No solution 
A)    
B)    
C)    
D) The equations are dependent 
E) No solution

Question 5

Solve the system using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent. 
A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent.

Question 6

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 7

Find a system of inequalities for the graph shown.

Accepted Answer

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

Question 8

A hospital dietician wishes to prepare a corn-squash vegetable dish that will provide at least   grams of protein and cost no more than   cents per serving. An ounce of creamed corn provides   gram of protein and costs   cents. An ounce of squash supplies   gram of protein and costs   cents. For taste, there must be at least   ounces of corn and at least as much squash as corn. It is important to keep the total number of ounces in a serving as small as possible. Find the combination of corn and squash that will minimize the amount of ingredients used per serving.

Accepted Answer

A)    ounces of corn and   ounces of squash 
B)    ounces of corn and   ounces of squash 
C)    ounces of corn and   ounces of squash 
D)    ounces of corn and   ounces of squash 
E)    ounces of corn and   ounces of squash 
A)    ounces of corn and   ounces of squash 
B)    ounces of corn and   ounces of squash 
C)    ounces of corn and   ounces of squash 
D)    ounces of corn and   ounces of squash 
E)    ounces of corn and   ounces of squash

Question 9

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 7, -18 ) 
B) ( 9, 14 ) 
C) ( - 7, -18 ), ( 9, 14 ) 
D) ( - 7, -18 ), ( 8, 14 ) 
E) no solution 
A) ( - 7, -18 ) 
B) ( 9, 14 ) 
C) ( - 7, -18 ), ( 9, 14 ) 
D) ( - 7, -18 ), ( 8, 14 ) 
E) no solution

Question 10

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 3, -16 ) 
B) ( - 3, -16 ), ( 6, 11 ) 
C) ( 6, 11 ) 
D) ( - 3, -16 ), ( 5, 11 ) 
E) no solution 
A) ( - 3, -16 ) 
B) ( - 3, -16 ), ( 6, 11 ) 
C) ( 6, 11 ) 
D) ( - 3, -16 ), ( 5, 11 ) 
E) no solution

Question 11

Solve the system   using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent 
A)    
B)    
C)    
D) The system is inconsistent 
E) The equations are dependent

Question 12

Solve the system using the inverse method.

Accepted Answer

A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent. 
A)    
B)    
C)    
D) The system is inconsistent. 
E) The equations are dependent.

Question 13

Let   be the identity matrix of order 2, and let   . Find the polynomial   for the given matrix A in order to find the zeros of   .
(In the study of matrices,   is the characteristic polynomial of A, and the zeros of   are the characteristic values (eigenvalues) of A.)

Accepted Answer

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

Question 14

Use the method of substitution to solve the system.

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 15

Find the determinant of the matrix.

Accepted Answer

A) -1083.6 
B) -173 
C) -433.44 
D) -443.44 
A) -1083.6 
B) -173 
C) -433.44 
D) -443.44

Question 16

Use Cramer's rule, whenever possible, to solve the system.

Accepted Answer

A)    
B)    
C)    
D) The equations are dependent. 
E) The system is inconsistent. 
A)    
B)    
C)    
D) The equations are dependent. 
E) The system is inconsistent.

Question 17

Find the partial fraction decomposition.

Accepted Answer

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

Question 18

Find the inverse of the matrix if it exists.

Accepted Answer

A)    
B)    
C)    
D)    
E) Does not exist 
A)    
B)    
C)    
D)    
E) Does not exist

Question 19

A shop specializes in preparing blends of gourmet coffees. From Colombian, Costa Rican, and Kenyan coffees, the owner wishes to prepare 2-pounds bags that will sell for $8.50. The cost per pound of these coffees is $10, $6, and $8, respectively. The amount of Colombian is to be three times the amount of Costa Rican. Find the amount of each type of coffee in the blend.

Accepted Answer

A) 0.3 lb Colombian , 0.1 lb Costa Rican , 1.6 lb Kenyan 
B) 1.05 lb Colombian , 0.35 lb Costa Rican , 0.6 lb Kenyan 
C) 0.6 lb Colombian , 0.2 lb Costa Rican , 1.2 lb Kenyan 
D) 0.75 lb Colombian , 0.25 lb Costa Rican , 2 lb Kenyan 
E) 0.75 lb Colombian , 0.25 lb Costa Rican , 1 lb Kenyan 
A) 0.3 lb Colombian , 0.1 lb Costa Rican , 1.6 lb Kenyan 
B) 1.05 lb Colombian , 0.35 lb Costa Rican , 0.6 lb Kenyan 
C) 0.6 lb Colombian , 0.2 lb Costa Rican , 1.2 lb Kenyan 
D) 0.75 lb Colombian , 0.25 lb Costa Rican , 2 lb Kenyan 
E) 0.75 lb Colombian , 0.25 lb Costa Rican , 1 lb Kenyan

Question 20

Find the determinant of the matrix after introducing zeros.

Accepted Answer

A) 0 
B) - 53 
C) 51 
D) - 52 
E) - 54 
A) 0 
B) - 53 
C) 51 
D) - 52 
E) - 54

Find the inverse of the matrix if it exists.

Solve the system using the inverse method.

Solve the system using the inverse method.

Use matrices to solve the system.

Solve the system using the inverse method.

Solve the system using the inverse method.

Find a system of inequalities for the graph shown.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Solve the system using the inverse method.

Solve the system using the inverse method.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Use Cramer's rule, whenever possible, to solve the system.

Find the partial fraction decomposition. $Find the partial fraction decomposition.$

Find the inverse of the matrix if it exists.

Find the determinant of the matrix after introducing zeros.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Exam 9: Systems of Equations and Inequalities

Find the inverse of the matrix if it exists.

Solve the system using the inverse method.

Solve the system using the inverse method.

Use matrices to solve the system.

Solve the system using the inverse method.

Solve the system using the inverse method.

Find a system of inequalities for the graph shown.

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Solve the system using the inverse method.

Solve the system using the inverse method.

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A in order to find the zeros of . (In the study of matrices, is the characteristic polynomial of A, and the zeros of are the characteristic values (eigenvalues) of A.)

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Use Cramer's rule, whenever possible, to solve the system.

Find the partial fraction decomposition.

Find the inverse of the matrix if it exists.

Find the determinant of the matrix after introducing zeros.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Sequences, Series and Probability

Topics From Analytic Geometry

Filters

Find the partial fraction decomposition. $Find the partial fraction decomposition.$