Question 1

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 2

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

Accepted Answer

To find the matrix sum, we add the corresponding elements of each matrix. In this case, we can see that the first three groups of digits in all three matrices are the same, so we can ignore them. Adding the fourth group of digits for each matrix gives us: 2ada + 2adb = 51ec. Solving for the missing digit in the sum, we get 51ec - 2ada = a00e. Therefore, the correct matrix sum is 11ea984b_ae88_a00e_9029_3b35f1723339_TB4005_11, which corresponds to choice C.

Question 3

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 4

​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?
​

Accepted Answer

To find the sum of each row in the matrix A+B, we add the corresponding entries in A and B.

Row 1: (0+1), (2+0), (1+1), (1+0), (0+1) = 2,2,2
Row 2: (1+0), (0+2), (0+0), (0+2), (1+0) = 1,2,0
Row 3: (0+1), (0+0), (2+0), (1+1), (1+0) = 1,0,2
Row 4: (2+0), (2+0), (1+0), (0+1), (0+0) = 2,2,1
Row 5: (1+0), (1+1), (1+1), (2+0), (0+0) = 1,2,2

From this, we can see that the sum of row 2 is the smallest (1+2+0=3), making player 2 the least likely top-ranked player. The sum of row 3 is the largest (1+0+2=3), making player 3 the most likely top-ranked player. Therefore, the answer is A) player 3.

Question 5

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

Accepted Answer

We can use the formula DE = BA - CD, where A, B, C, D are the matrices given.

DE =

| 2  1  5 |   | 1 -1  3 |   | 4 -1 |
| 3 -4  0 | - | 2  2 -1 | * |-1  2 |

=

| (2*1 + 1*2 + 5*(-1))  (-2 -1 -3)   (2*3 + 1*(-1) + 5*2) |
| (3*1 - 4*2 + 0*(-1))  (-3 -8  2)   (3*3 - 4*(-1) + 0*2) |

=

| -2 -6 13 |
| -5 -9 13 |

Therefore, the correct choice is C.

Question 6

​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. ​

Accepted Answer

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

Question 7

Multiply the matrices. ​  ​

Accepted Answer

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

Question 8

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

Accepted Answer

BE cannot be found from the given matrices as they are not square matrices and their dimensions do not match for multiplication. Therefore, the answer is that BE is undefined.

Question 9

Multiply the matrices. ​  ​

Accepted Answer

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

Question 10

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 answer of The figure that follows depicts the mean...

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. If ALCO pays 35% of the amount owed on each debt, write the matrix giving the remaining debts. ​
​   ​

Accepted Answer

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

Question 12

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

Accepted Answer

Let A = first matrix = 11ea984b_ae85_6b99_9029_6556ee6a93f3_TB4005_11
Let B = second matrix = 11ea984b_ae85_92aa_9029_4952708ccc08_TB4005_11

To find CD, we need to multiply A and B in the order CD (not DC as matrix multiplication is not commutative).

Multiplying A and B, we get:

A x B = 
[ 1 0 0 1 ] [ 1 1 2 1 ] = [ 2 1 2 2 ]
[ 0 1 1 0 ] [ 2 1 0 1 ]   [ 1 1 1 0 ]
[ 0 0 1 1 ] [ 1 2 1 0 ]   [ 1 1 1 1 ]
[ 0 1 0 0 ] [ 0 0 1 1 ]   [ 1 0 0 0 ]

So, CD = [ 2 1 2 2 ; 1 1 1 0 ; 1 1 1 1 ; 1 0 0 0 ]

The correct answer choice is D.

Question 13

The matrix that follows represents work efficiency for workers at nine different work centers. Suppose that the work centers changes in rules cause efficiency to decrease by 0.04 at work centers 2 and 5 and to decrease by 0.01 at work center 7. Write the matrix that describes the new efficiencies.​ ​
  ​

Accepted Answer

The answer of The matrix that follows represents work efficiency...

Question 14

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

Accepted Answer

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

Question 15

​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

To find the remaining debt, we need to subtract the amount paid (20%) from the amount owed. The resulting matrix would be:

| A: | 20% of 50000 | 20% of 40000 | 20% of 30000 |
| B: | 20% of 25000 | 20% of 20000 | 20% of 15000 |
| C: | 20% of 10000 | 20% of 8000  | 20% of 6000  |

Simplifying the expression, we get:

| A: | 10000 | 8000 | 6000 |
| B: | 5000  | 4000 | 3000 |
| C: | 2000  | 1600 | 1200 |

Therefore, the answer is option B.

Question 16

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...

Question 17

​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. ​​

Accepted Answer

Based on the diagram, player 3 has defeated player 4, and player 4 has defeated player 5. Therefore, player 3 should be ranked higher than player 4 and player 5. Player 1 has defeated player 3 and player 4, so they should be ranked higher than those two players. Finally, player 2 has defeated player 1, so player 2 should be ranked highest. This ranking order is consistent with option C.

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

The matrices have different numbers of columns, so matrix multiplication is undefined. Therefore, we cannot find EC.

Question 20

Multiply the matrices.  ​

Accepted Answer

The answer of Multiply the matrices.  ​
...

Quiz 3: Matrices

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

Use the matrices to find DE, 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. ​

Multiply the matrices. ​ ​

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

Multiply the matrices. ​ ​

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

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

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. ​​

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

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

Multiply the matrices. ​

Use the matrices to find , if possible.

Use the matrices to find DE, 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.

Multiply the matrices.

Use the matrices to find BE, if possible.

Multiply the matrices.

Use the matrices to find CD, if possible.

Use the matrices to find CF, if possible.

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.

Use the matrices to find BA, if possible.

Use the matrices to find EC, if possible.

Multiply the matrices.