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.)

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Question 2

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

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Question 3

Solve the system using the inverse method.

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The answer of Solve the system using the inverse method....

Question 4

Use matrices to solve the system.

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The answer of Use matrices to solve the system. 
...

Question 5

Solve the system  using the inverse method.

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The answer of Solve the system  using the inverse...

Question 6

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

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Question 7

Solve the system.

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The answer of Solve the system. 
...

Question 8

Use matrices to solve the system.

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The answer of Use matrices to solve the system. 
...

Question 9

Use the method of substitution to solve the system.

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Question 10

A stationary company makes two types of notebooks: a deluxe notebook with subject dividers, which sells for $1.2, and a regular notebook, which sells for $0.85. The production cost is $1.00 for each deluxe notebook and $0.75 for each regular notebook. The company has the facilities to manufacture between 2,000 and 3,000 deluxe and between 3,000 and 6,000 regular notebooks, but not more than 8,000 altogether. How many notebooks of each type should be manufactured to maximize the difference between the selling prices and the production cost?

Accepted Answer

To maximize profit, the company should produce the maximum number of notebooks within the constraints. Producing 3,000 deluxe and 5,000 regular notebooks maximizes the total number (8,000) while ensuring the highest profit margin per unit.

Question 11

Solve the system  using the inverse method.

Accepted Answer

The answer of Solve the system  using the inverse...

Question 12

Three average monthly low temperatures for Detroit are listed in the table. 
Let  correspond to January,  to February, . . . , and  to December. Determine a quadratic function  that interpolates the data - that is, determine the constants a, b, and c such that  , and  .

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The answer of Three average monthly low temperatures for Detroit...

Question 13

Use the method of substitution to solve the system.

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The answer of Use the method of substitution to solve...

Question 14

Use the method of substitution to solve the system.

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The answer of Use the method of substitution to solve...

Question 15

Find the determinant of the matrix.

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The answer of Find the determinant of the matrix. 
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Question 16

Use the method of substitution to solve the system.

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The answer of Use the method of substitution to solve...

Question 17

A small firm manufactures bookshelves and desks for microcomputers. For each product it is necessary to use a table saw and a power router. To manufacture each bookshelf, the saw must be used for  hour and the router for 1 hour. A desk requires the use of each machine for 2 hours. The profits are $20 per bookshelf and $50 per desk. If the saw can be used for 8 hours per day and the router for 12 hours per day, how many bookshelves and desks should be manufactured each day to maximize the profit?

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Question 18

Find the determinant.

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The answer of Find the determinant. 
...

Question 19

A manufacturer of cell phones makes a profit of $24 on a deluxe model and $30 on a standard model. The company wishes to produce at least 80 deluxe models and at least 100 standard models per day. To maintain high quality, the daily production should not exceed 200 phones. How many of each type should be produced daily in order to maximize the profit?

Accepted Answer

To maximize profit while meeting the production constraints, linear programming can be used. The constraints are at least 80 deluxe models and at least 100 standard models, with a total not exceeding 200 phones daily. The profit function to maximize is $24 per deluxe model plus $30 per standard model. Without solving the entire linear programming problem here, choice A, 120 standard and 80 deluxe, fits within the constraints and suggests a high-profit mix given the profit rates and constraints provided.

Question 20

Find a system of inequalities for the graph shown.

Accepted Answer

The answer of Find a system of inequalities for the...

Quiz 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.)

Sketch the region R determined by the given constraints, and label its vertices. Find the maximum value of C on R.

Solve the system using the inverse method.

Use matrices to solve the system.

Solve the system using the inverse method.

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

Solve the system.

Use matrices to solve the system.

Use the method of substitution to solve the system.

Solve the system using the inverse method.

Three average monthly low temperatures for Detroit are listed in the table. Let correspond to January, to February, . . . , and to December. Determine a quadratic function that interpolates the data - that is, determine the constants a, b, and c such that , and .

Use the method of substitution to solve the system.

Use the method of substitution to solve the system.

Find the determinant of the matrix.

Use the method of substitution to solve the system.

Find the determinant.

Find a system of inequalities for the graph shown.