Question 1

Write the matrix equation as a system of linear equations without matrices:
-

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 2

A message has been encoded and the matrix which the receiver gets is shown below.   The encoding matrix A which was used to encode the message is:A =   Find the decoding matrix A-1, and use it to decode the message.Assume that the numerical assignment used was a = 1, b = 2, ....., z = 26, space = 30, period = 40, and apostrophe = 60.

Accepted Answer

A)  DRINK ENOUGH COKE 
B)  DRINK ENOUGH MILK 
C)  EAT YOUR VEGETABLES 
D)  EAT YOUR BROCCOLI 
A)  DRINK ENOUGH COKE 
B)  DRINK ENOUGH MILK 
C)  EAT YOUR VEGETABLES 
D)  EAT YOUR BROCCOLI

Question 3

Solve the system as matrix equations using inverses:
-

Accepted Answer

A)  (3,2) 
B)  (-2, -3) 
C)  (-3 , - 2) 
D)  (2,3) 
A)  (3,2) 
B)  (-2, -3) 
C)  (-3 , - 2) 
D)  (2,3)

Question 4

A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier X?

Accepted Answer

A)  $3300 
B)  $4800 
C)  $6600 
D)  $7800 
A)  $3300 
B)  $4800 
C)  $6600 
D)  $7800

Question 5

A paper company produces high, medium, and low grade paper. The number of tons of each grade that is produced from one ton of pulp depends on the source of that pulp. The following table lists three sources and the amount of each grade of paper that can be made for one ton of pulp from each source.
   
The paper company has orders for 11 tons of high grade, 15 tons of medium grade, and 14 tons of low grade paper. How many tons of each type of pulp should be used to fill these orders exactly? Set up a system of linear equations, letting x, y, and z be the number of tons of Brazilian pulp, domestic pulp, and recycled pulp, respectively, needed to fill the orders.

Accepted Answer

The answer of A paper company produces high, medium, and...

Question 6

Solve the system of equations by substitution:
-

Accepted Answer

A)  ( 2, 1) 
B)  ( -6, 1) 
C)  ( 1, 2) 
D)  ( -2, 1) 
A)  ( 2, 1) 
B)  ( -6, 1) 
C)  ( 1, 2) 
D)  ( -2, 1)

Question 7

Perform the indicated operations given the matrices:
-

Accepted Answer

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

Question 8

Perform the operation, if possible:
-

Accepted Answer

The answer of Perform the operation, if possible:
- ...

Question 9

Perform the indicated operations given the matrices:
-

Accepted Answer

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

Question 10

Find the inverse, if it exists, of the given matrix:
-A =

Accepted Answer

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

Question 11

Find the values of a, b, c, and d that make the matrix equation true.
-

Accepted Answer

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

Question 12

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed:
-Solve for Y: XY + ZY = A

Accepted Answer

A)  Y = (X + Z)-1 A 
B)  Y = X-1(A - ZY) 
C)  Y = X-1(A - Z) 
D)  Y =  A(X + Z)-1  
A)  Y = (X + Z)-1 A 
B)  Y = X-1(A - ZY) 
C)  Y = X-1(A - Z) 
D)  Y =  A(X + Z)-1

Question 13

Given matrix A:   What is the size of A?

Accepted Answer

A)  3 × 3 
B)  3 × 2 
C)  2 × 3 
D)  3 
A)  3 × 3 
B)  3 × 2 
C)  2 × 3 
D)  3

Question 14

Write the augmented matrix for the system.

Accepted Answer

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

Question 15

Perform the operation, if possible:
-

Accepted Answer

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

Write the matrix equation as a system of linear equations without matrices: -

Solve the system as matrix equations using inverses: -

A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier X?

Solve the system of equations by substitution: -

Perform the indicated operations given the matrices: -

Perform the operation, if possible: -

Perform the indicated operations given the matrices: -

Find the inverse, if it exists, of the given matrix: -A =

Find the values of a, b, c, and d that make the matrix equation true. -

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed: -Solve for Y: XY + ZY = A

Given matrix A: What is the size of A?

Write the augmented matrix for the system.

Perform the operation, if possible: -

Linear Equations and Graphs

Functions and Graphs

Mathematics of Finance

Linear Inequalities and Linear Programming

Linear Programming: The Simplex Method

Logic, Sets, and Counting

Probability

Markov Chains

Data Description and Probability Distributions

Games and Decisions

Appendix A: Basic Algebra Review

Appendix B: Special Topics

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Exam 4: Systems of Linear Equations; Matrices

Write the matrix equation as a system of linear equations without matrices: -

Solve the system as matrix equations using inverses: -

A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier X?

Solve the system of equations by substitution: -

Perform the indicated operations given the matrices: -

Perform the operation, if possible: -

Perform the indicated operations given the matrices: -

Find the inverse, if it exists, of the given matrix: -A =

Find the values of a, b, c, and d that make the matrix equation true. -

Solve the equation for the indicated variable. Assume that the dimensions are such that matrix multiplication and addition are possible and that inverses exist when needed: -Solve for Y: XY + ZY = A

Given matrix A: What is the size of A?

Write the augmented matrix for the system.

Perform the operation, if possible: -

Linear Equations and Graphs

Functions and Graphs

Mathematics of Finance

Linear Inequalities and Linear Programming

Linear Programming: The Simplex Method

Logic, Sets, and Counting

Probability

Markov Chains

Data Description and Probability Distributions

Games and Decisions

Appendix A: Basic Algebra Review

Appendix B: Special Topics

Filters