Question 1

Solve the system of linear equations using the Gauss-Jordan elimination method.

Accepted Answer

A)  ( 5, -2, -3 ) 
B)  ( 3, -2, -5 ) 
C)  ( -5, 3, 5 ) 
D)  ( 2, -3, 5 ) 
E)  ( 2, 3, 5 ) 
A)  ( 5, -2, -3 ) 
B)  ( 3, -2, -5 ) 
C)  ( -5, 3, 5 ) 
D)  ( 2, -3, 5 ) 
E)  ( 2, 3, 5 )

Question 2

A dietitian wishes to plan a meal around three foods. The meal is to include   units of vitamin A,   units of vitamin C, and   units of calcium. The number of units of the vitamins and calcium in each ounce of the foods is summarized in the accompanying table. Show that such a meal cannot be planned around the foods.
​

Accepted Answer

We must solve the following system of li

Question 3

Solve the matrix equation   for the given matrices A, D and X.
​   ​
Round each number to two decimal places, if necessary.
​
x = __________
​
y = __________

Accepted Answer

The answer of Solve the matrix equation   for...

Question 4

Solve the system of equations by using the inverse of the coefficient matrix. where   ,   ,   .

Accepted Answer

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

Question 5

The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $38 and $30/acre, respectively. Jacob Johnson has $16,600 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? ​

Accepted Answer

A)  250 acres of corn and 300 acres of wheat 
B)  300 acres of corn and 200 acres of wheat 
C)  450 acres of corn and 50 acres of wheat 
D)  200 acres of corn and 300 acres of wheat 
E)  200 acres of corn and 350 acres of wheat 
A)  250 acres of corn and 300 acres of wheat 
B)  300 acres of corn and 200 acres of wheat 
C)  450 acres of corn and 50 acres of wheat 
D)  200 acres of corn and 300 acres of wheat 
E)  200 acres of corn and 350 acres of wheat

Question 6

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​  ...

Question 7

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​

Accepted Answer

A)  20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee 
B)  75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee 
C)  80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee 
D)  80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee 
E)  85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee 
A)  20 lb of $3.00/lb coffee and 80 lb of $2.50/lb coffee 
B)  75 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee 
C)  80 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee 
D)  80 lb of $3.00/lb coffee and 25 lb of $2.50/lb coffee 
E)  85 lb of $3.00/lb coffee and 20 lb of $2.50/lb coffee

Question 8

Formulate but do not solve the problem. Michael Perez has a total of $1,100 on deposit with two savings institutions. One pays interest at the rate of 7%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $82 in interest during a single year, how much does he have on deposit in each institution? Let x be the amount of money in saving institution with interest at the rate of 7%/year.

Accepted Answer

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

Question 9

Lawnco produces three grades of commercial fertilizers. A 100-lb bag of grade-A fertilizer contains   lb of nitrogen,   lb of phosphate, and   lb of potassium. A 100-lb bag of grade-B fertilizer contains   lb of nitrogen and   lb each of phosphate and potassium. A 100-lb bag of grade-C fertilizer contains   lb of nitrogen,   lb of phosphate, and   lb of potassium. How many 100-lb bags of each of the three grades of fertilizers should Lawnco produce if   lb of nitrogen,   lb of phosphate, and   lb of potassium are available and all the nutrients are used?

Accepted Answer

A)    ,   and   100-lb bags correspondingly 
B)    ,   and   100-lb bags correspondingly 
C)    ,   and   100-lb bags correspondingly 
D)    ,   and   100-lb bags correspondingly 
E)  the problem has no solution 
A)    ,   and   100-lb bags correspondingly 
B)    ,   and   100-lb bags correspondingly 
C)    ,   and   100-lb bags correspondingly 
D)    ,   and   100-lb bags correspondingly 
E)  the problem has no solution

Question 10

Solve the matrix equation   for the matrices A and D.

Accepted Answer

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

Question 11

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. If not, answer inconsistent.

Accepted Answer

The answer of Given that the augmented matrix in row-reduced...

Question 12

Compute the product. ​   ​

Accepted Answer

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

Question 13

Compute the product. ​   ​

Accepted Answer

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

Question 14

Identify the square matrix. What is its transpose?

Accepted Answer

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

Question 15

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Accepted Answer

The answer of Writing a matrix equation that is equivalent...

Question 16

Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution? ​

Accepted Answer

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

Question 17

Find b13, b31 and b43.

Accepted Answer

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

Question 18

Bond Brothers, a real estate developer, builds houses in three states. The projected number of units of each model to be built in each state is given by the matrix   The profits to be realized are $19,000, $22,000, $25,000, and $30,000, respectively, for each model I, II, III, and IV house sold. Find the total profit Bond Brothers expects to earn in each state if all the houses are sold.
profit in N.Y. $__________
profit in Conn. $__________
profit in Mass. $__________
total profit $__________

Accepted Answer

7,150,000;

Question 19

Compute the product.
​

Accepted Answer

The answer of Compute the product.
​  ...

Question 20

A simple economy consists of three sectors: agriculture (A), manufacturing (M), and transportation (T). The input-output matrix for this economy is given by
​
A M T   If the units are measured in millions of dollars, determine the amount of agricultural products consumed in the production of $300 million worth of manufactured goods.
$ __________ million

Accepted Answer

The answer of A simple economy consists of three sectors:...

Solve the system of linear equations using the Gauss-Jordan elimination method.

Solve the matrix equation for the given matrices A, D and X. Round each number to two decimal places, if necessary. x = y =

Solve the system of equations by using the inverse of the coefficient matrix. where , , .

Compute the product.

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)

Solve the matrix equation for the matrices A and D.

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. If not, answer inconsistent.

Compute the product.

Compute the product.

Identify the square matrix. What is its transpose?

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Michael Perez has a total of $2,000 on deposite with two savings institutions. One pays interest at the rate of 6%/year, whereas the other pays interest at the rate of 8%/year. If Michael earned a total of $144 in interest during a single year, how much does he have on deposite in each institution?

Find b₁₃, b₃₁ and b₄₃.

Compute the product.

Straight Lines and Linear Functions

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Exam 2: Systems of Linear Equations and Matrices

Solve the system of linear equations using the Gauss-Jordan elimination method.

Solve the matrix equation for the given matrices A, D and X. ​ ​ Round each number to two decimal places, if necessary. ​ x = __________ ​ y = __________

Solve the system of equations by using the inverse of the coefficient matrix. where , , .

Compute the product. ​

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.) ​

Solve the matrix equation for the matrices A and D.

Given that the augmented matrix in row-reduced form is equivalent to the augmented matrix of a system of linear equations, determine whether the system has a solution and find the solution or solutions to the system, if they exist. If not, answer inconsistent.

Compute the product. ​ ​

Compute the product. ​ ​

Identify the square matrix. What is its transpose?

Writing a matrix equation that is equivalent to the given system of linear equations, solve the system using the inverse matrix.

Find b13, b31 and b43.

Compute the product. ​

Straight Lines and Linear Functions

Linear Programming: a Geometric Approach

Linear Programming: an Algebraic Approach

Mathematics of Finance

Sets and Counting

Probability

Probability Distributions and Statistics

Markov Chains and the Theory of Games

Filters

Solve the matrix equation for the given matrices A, D and X. Round each number to two decimal places, if necessary. x = y =

Compute the product.

The Coffee Shoppe sells a coffee blend made from two coffees, one costing $3.00/lb and the other costing $2.50/lb. If the blended coffee sells for $2.90/lb, find how much of each coffee is used to obtain the desired blend. (Assume the weight of the blended coffee is 100 lb.)

Compute the product.

Compute the product.

Find b₁₃, b₃₁ and b₄₃.

Compute the product.