Question 1

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​  Construct matrix A with elements  .
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Accepted Answer

The answer of In order to rank the five members...

Question 2

Use matrix A to find A², if possible.

Accepted Answer

The answer of Use matrix A to find A², if...

Question 3

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​
1  2    5    3  4
​Construct matrix B with elements  .
​

Accepted Answer

The answer of ​In order to rank the five members...

Question 4

Use the matrices to find CD, if possible. ​   ​

Accepted Answer

The answer of Use the matrices to find CD, if...

Question 5

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​​  Let matrix A represent the matrix with the following elements:  .
Let matrix B represent the matrix with the following elements:  .
The player i is the top-ranked player if the sum of row i in the matrix A + B is the largest. What is the number of this player?
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Accepted Answer

The answer of ​In order to rank the five members...

Question 6

Use the matrices to find  , if possible. ​   ​

Accepted Answer

The answer of Use the matrices to find  ,...

Question 7

​When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. Suppose Maxx Industries pays 20% of the amount owed on each loan. Write the matrix that would give the remaining debt in each category. ​

Accepted Answer

The answer of ​When a firm buys another company, the...

Question 8

Use the matrices to find CF, if possible. ​
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Accepted Answer

The answer of Use the matrices to find CF, if...

Question 9

Multiply the matrices.  ​

Accepted Answer

To multiply two matrices, the number of columns of the first matrix must be equal to the number of rows of the second matrix. In this case, the first matrix has 2 rows and 3 columns, while the second matrix has 3 rows and 1 column, so we can multiply them. The result will be a matrix with 2 rows and 1 column, which is option B.

Question 10

Use the matrices to find BA, if possible. ​
​   ​

Accepted Answer

The answer of Use the matrices to find BA, if...

Question 11

Ace, Baker, and Champ are being purchased by ALCO, Inc., and their outstanding debts must be paid by the purchaser. The matrix below gives the amounts of debt and the terms for the companies being purchased. Suppose ALCO decides to pay 80% of all debts due in 30 days and to increase the debts due in 60 days by 20%. Write a matrix that gives the debts after these transactions are made. ​
​   ​

Accepted Answer

The answer of Ace, Baker, and Champ are being purchased...

Question 12

Use the matrices to find DE, if possible. ​
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Accepted Answer

To find DE, we multiply matrices D and E in the same order as they are written, that is DE. However, the dimensions of these matrices are not compatible for multiplication. The number of columns in D must match the number of rows in E. Since D has 3 columns and E has 2 rows, we cannot directly multiply D and E. Therefore, DE is undefined.

Question 13

Use the matrices to find  , if possible. ​   ​
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Accepted Answer

The answer of Use the matrices to find  ,...

Question 14

The figure that follows depicts the mean (average) flow time for a job when the critical-ratio rule is used to dispatch workers at several machines required to complete the job. In the figure, WHN 1, WHN 2, and WHN 3 represent three different rules for determining when a worker should be transferred to another machine, and Where represents six rules for determining the machine to which the worker is transferred. Construct a 3×6 matrix A to represent these data, with entries rounded to the nearest integer. ​  ​

Accepted Answer

The 3 x 6 matrix A should have entries rounded to the nearest integer, so we need to look at the figure and round each entry to the nearest integer. For example, the entry corresponding to WHN 1 and Where 1 is about 25.5, which should be rounded to 26. Similarly, we can round all the other entries and get the following matrix:

| 27 | 26 | 26 | 27 | 27 | 27 |
|----|----|----|----|----|----|
| 27 | 26 | 26 | 27 | 27 | 27 |
| 29 | 28 | 27 | 28 | 28 | 28 |

Therefore, the correct choice is B.

Question 15

Use the matrices to find BE, if possible. ​   ​

Accepted Answer

The matrices given do not have a common size or dimensions that allow for matrix multiplication. Therefore, BE cannot be found.

Question 16

Use the matrices to find EC, if possible. ​
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Accepted Answer

EC cannot be found as the matrices have different dimensions.

Question 17

Multiply the matrices. ​  ​

Accepted Answer

The answer of Multiply the matrices. ​  ​
...

Question 18

When a firm buys another company, the company frequently has some outstanding debt that the purchaser must pay. Consider three companies, A, B, and C, that are purchased by Maxx Industries. The following table gives the amount of each company's debt, classified by the number of days remaining until the debt must be paid. What payment plan did Maxx Industries use if the outstanding debt is given by the following matrix? ​   ​

Accepted Answer

The answer of When a firm buys another company, the...

Question 19

Multiply the matrices. ​  ​

Accepted Answer

The answer of Multiply the matrices. ​  ​
...

Question 20

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient? ​  ​

Accepted Answer

The answer of Use a computer spreadsheet to find the...

Quiz 4: Matrices

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. Construct matrix A with elements .

Use matrix A to find A², if possible.

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. 1 2 5 3 4 Construct matrix B with elements .

Use the matrices to find CD, if possible.

Use the matrices to find , if possible.

Use the matrices to find CF, if possible.

Multiply the matrices.

Use the matrices to find BA, if possible.

Use the matrices to find DE, if possible.

Use the matrices to find , if possible.

Use the matrices to find BE, if possible.

Use the matrices to find EC, if possible.

Multiply the matrices.

Multiply the matrices.

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient?

Quiz 4: Matrices

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​ Construct matrix A with elements . ​

Use matrix A to find A2, if possible. ​ ​

​In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. ​ 1 2 5 3 4 ​Construct matrix B with elements . ​

Use the matrices to find CD, if possible. ​ ​

Use the matrices to find , if possible. ​ ​

Use the matrices to find CF, if possible. ​ ​ ​ ​

Multiply the matrices. ​

Use the matrices to find BA, if possible. ​ ​ ​

Use the matrices to find DE, if possible. ​ ​ ​ ​

Use the matrices to find , if possible. ​ ​ ​

Use the matrices to find BE, if possible. ​ ​

Use the matrices to find EC, if possible. ​ ​ ​ ​

Multiply the matrices. ​ ​

Multiply the matrices. ​ ​

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient? ​ ​

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. Construct matrix A with elements .

Use matrix A to find A², if possible.

In order to rank the five members of its chess team for play against another school, the coach draws the following diagram. An arrow from 1 to 2 means player 1 has defeated player 2. 1 2 5 3 4 Construct matrix B with elements .

Use the matrices to find CD, if possible.

Use the matrices to find , if possible.

Use the matrices to find CF, if possible.

Multiply the matrices.

Use the matrices to find BA, if possible.

Use the matrices to find DE, if possible.

Use the matrices to find , if possible.

Use the matrices to find BE, if possible.

Use the matrices to find EC, if possible.

Multiply the matrices.

Multiply the matrices.

Use a computer spreadsheet to find the average efficiency for each work center over the first five workers. Which work center is the most efficient?