Question 1

Let  be the identity matrix of order 2, and let  . Find the polynomial  for the given matrix A. (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)

Question 2

Use the method of substitution to solve the system.

Accepted Answer

A) ( - 4, -21 ) 
B) ( - 4, -21 ), ( 9, 44 ) 
C) ( - 4, -21 ), ( 8, 44 ) 
D) ( 9, 44 ) 
E) no solution

Question 3

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

Question 4

Find the inverse of the matrix if it exists.

Accepted Answer

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

Question 5

Use matrices to solve the system.

Accepted Answer

A)   
B)   
C)   
D) The system is dependent 
E) No solution

Question 6

Solve the system.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 7

Use the method of substitution to solve the system.

Accepted Answer

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

Exam 9: Systems of Equations and Inequalities

Let be the identity matrix of order 2, and let . Find the polynomial for the given matrix A. (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 inverse of the matrix if it exists.

Use matrices to solve the system.

Solve the system.

Use the method of substitution to solve the system.