# Show that the set of vectors {(−4,1,3),(5,1,6),(6,0,2)} does not span R 3 , but that it does span the subspace of R 3 consisting of all vectors lying in the plane with equation x + 13y − 3z = 0.

The vectors does not span R3 and only span a subspace of R3 which satisfies x+13y-3z=0

Explanation:

The vectors are given as

Now if the vectors  would span the , the rank of  the consolidated matrix will be 3 if it is not 3 this indicates that the vectors does not span the .

So the matrix is given as

In order to calculate the rank, the matrix is reduced to the Row Echelon form as

As the Rank is given as number of non-zero rows in the Row echelon form which are 2 so the rank is 2.

Thus this indicates that the vectors does not span

Now for any vector the corresponding equation is formulated by using the combined matrix which is given as  for any arbitrary vector and the coordinate as

Now converting the combined matrix as

From this it is seen that whatever the values of the coordinates does not effect the value of the plane with equation as

So it is verified that the subspace of R3 such that it satisfies x+13y-3z=0 consists of all vectors.

## Related Questions

Bailey enjoys working with her hands. She wants to choose a career path that would allow her to create things. Which career would be best for her? zoologist greenhouse nursery worker energy auditor civil engineer jeweler and metal worker

Given that Bailey enjoys working with her hands the career that is going to be best for her would be the jeweler and metal worker.

Who is a  jeweler and metal worker?

This is the term that is used to refer to the business that involves a person that is into the creation of jewelry from precious stones as well as the use of precious metals. He does this in such a way that he is able to examine and also grade diamonds as well as other precious stones. This is the career path that is best for her because it involves creativity and the Jeweler is one that uses her hands to get the end product of what they want.

In summary we can say that Given that Bailey enjoys working with her hands the career that is going to be best for her would be the  jeweler and metal worker.

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One important way to become a respected team member in an organization is to a. form a sub-alliance within the team. b. go along with the team regardless of your personal feelings or ideas. c. express your own view. d. avoid self-disclosure.

Go along with the team regardless of your personal feelings or ideas is one important way to become a respected team member in an organization. Hence, option B is correct.

Why all the team member in organization should treat equally?

In an organization all the members must treat equally, this shows that the upper authority of the organization respects the lower staff and people.

It helps in building the reputation of the organization. Employees feel more blessed and kind to this gesture.

Thus, option B is correct.

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B

Explanation:

The best option is B, because it would turn you into a Leader, and not into a Boss. Leaders are respected, bosses are feared.

On April 1, 2016, the KB Toy Company purchased equipment to be used in its manufacturing process. The equipment cost \$57,200, has an ten-year useful life, and has no residual value. The company uses the straight-line depreciation method for all manufacturing equipment. On January 4, 2018, \$14,750 was spent to repair the equipment and to add a feature that increased its operating efficiency. Of the total expenditure, \$2,900 represented ordinary repairs and annual maintenance and \$11,850 represented the cost of the new feature. In addition to increasing operating efficiency, the total useful life of the equipment was extended to 12 years.

Required:

1. Prepare journal entries for the depreciation for 2016 and 2017.
2. Prepare journal entries for the 2018 expenditure.
3. Prepare journal entries for the depreciation for 2018.

2016 Depreciation

Dr depreciation expense \$5720

Cr Accumulated depreciation               \$5720

2017 Depreciation

Dr depreciation expense \$5720

Cr Accumulated depreciation               \$5720

Journal entries for 2018 expenditure

Dr repairs and maintenance   \$2900

Dr Equipment account             \$11850

Cr Cash account                                          \$14750

2018 Depreciation

Dr depreciation expense          \$4800.83

Cr Accumulated depreciation                     \$4800.83

Explanation:

There are two policies for depreciating non-current asset  especially when it is acquired part-way through the year like we have here, namely full year depreciation in the year of purchase and none in the year of disposal or proportional depreciation throughout the useful life,I am adopting the former in this question.

Formula for depreciation=cost-residual value/useful life

Yearly depreciation is (\$57200-\$0)/10=\$5720

However,after two years the book value is calculated thus:

Book value=\$57200-(\$5720*2)=\$45760

additional cost incurred in enhancing the capacity of the asset would be added :  \$45760 +\$11,850=\$57610

Since the useful life has also been reviewed up to 12 years, the depreciation from now on is \$57610/12=\$4800.83

1. Journal Entry for December 31, 2016

Depreciation Expense                                 Debit    \$ 4,290

Allowance for depreciation Equipment      Credit                     \$ 4,290

Journal Entry for December 31, 2017

Depreciation Expense                                 Debit     \$ 5,720

Allowance for depreciation Equipment      Credit                     \$ 5,720

Journal entry

2. Repairs and Maintenance Expense        Debit    \$ 2,900

Equipment                                                     Debit    \$ 11,850

Cash                                                               Credit                   \$ 14,750

3. Depreciation Expense                              Debit     \$ 5,904

Allowance for depreciation Equipment      Credit                     \$ 5,904

Explanation:

Computation of depreciation for 2016 and 2017

Original cost of equipment                                              \$ 57,200

Salvage Value                                                                  \$            0

Depreciable Basis                                                            \$ 57,200

Useful Life 10 years

Annual depreciation \$ 57,200 / 10 years \$ 5,720

Depreciation for 2016 from April - December 9 months          \$ 4,290

Depreciation for 2017 = Full Year                                               \$ 5,720

Computation of Depreciation for 2018

Depreciation for Jan to December 2018

Original Cost of equipment                                 \$ 57,200

Less: Depreciation for 1 year 9 months              \$ (10,010)

Net book value as at January 01 2018                \$ 47,190

Add: New Feature adding value to equipment  \$ 11,850

Revised Depreciation Base                                 \$ 59,040

Revised remaining useful life ( 12 - 2)                   10 years

Depreciation for full year                                      \$ 5,904

Depreciation for 2018                                                               \$ 5,904

Agribusinesses that sell commodity products such as wheat, rice, and corn are often in ________ position with their competitors. (A) an oligopolistic competition
(B) a monopolistic competition
(C) a monopolistic
(D) a pure competition
(E) a limited competition

The correct answer is letter "D": a pure competition.

Explanation:

A Pure or Perfect Competition is a theoretical framework of a market where competition is at its highest possible level. Many markets, such as stock exchanges and commodity markets, approach perfect competition, but it is unlikely that a real-life state of perfect competition will be attainable.

A house was purchased for \$350,000 in the year 2010. The value has been increasing by \$7,000 per year. Write the function and find the value of the house after 5 years.

When the original purchase value of the house in the year 2010 was \$350,000, and this value has been increasing by \$7,000 per year, then the future value of the house after 5 years will be \$385,000.

What is the significance of future value?

A future value can be referred to or considered as the value that a good or a commodity will have at the end of said number of periods, which is usually represented in terms of years. This future value is never based on assumptions.

For the above condition, the value increases by \$7,000 every year, so after 5 years it would increase by 7000×5 = \$35,000. Thus, the future value of the house will be computed as under,

Future Value = Original Value + Increase in Value

Future Value = 350,000 + 35,000

Future Value = \$385,000.

Therefore, the significance regarding a future value has been aforementioned.

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1757000

Explanation:

you wanna do y = 7,000x plus 350,000 times 5

Kai promised to repair Krystal's car on Thursday. After picking up the necessary part at a junkyard, he discovered he could not do the job after all and that the junkyard would not buy back the part. Krystal does not know about these developments. However, she thinks Kai will be finished with her car sometime today. What should Kai do? A. Try to repair the car even though he does not really know how.
B. Try to repair the car so he can at least get his money's worth out of it.
C. Call Krystal to inform her of the problem, and recommend a reputable repair shop.
D. Fake an emergency and contact Krystal on Monday.
E. Stall for time to read up on car repairs so he can practice on Krystal's car.

The answer is C. Call Krystal to inform her of the problem, and recommend a reputable repair shop.

Explanation:

Capricorn Creative Inc., a U.S.-based advertising firm, was the first in the advertising industry to identify the growth potential of Brazil and to make huge investments in its economy. As a result, the firm was able to build brand loyalty and gain experience in that country's business practices. In the language of business strategy, Capricorn Creative has typically benefited from

Explanation:

In business strategy, first mover advantage (FMA) refers to the competitive advantage that a company can acquire by being the first company to enter a new market or market segment. In order for this first entrance to be considered an advantage, the company must gain some control of resources or hold a significant position in the market.

For example, Microsoft introduced its Surface tablets before Apple introduced the iPad but it never gained a significant position in the market, so it never had a FMA.

Bank Management Printers Inc. produces luxury checkbooks with three checks and stubs per page. Each checkbook is designed for an individual customer and is ordered through the customer's bank. The company's operating budget for September 2014 includes this data: Number of Checkbooks: 15,000

Selling Price per book: \$20

Variable cost per book: \$8

Fixed costs for the month: \$145,000

The actual results for September 2015 were as follows:

Number of Checkbooks: 12,000

Selling Price per book: \$21

Variable cost per book: \$7

Fixed costs for the month: \$150,000

1. Prepare a static-budget based variance analysis of the September performance

2. Prepare a flexible budget based variance analysis of the September performance

3. Why might Bank Management find the flexible budget based variance analysis more informative than the static budget based variance analysis?

Explanation:

1. Prepare a static-budget based variance analysis of the September performance

Actual Static-Budget    Static

Results  Variances    Budget

-1 (2) = (1) – (3)             -3

Units sold                      12,000      3,000 U 15,000

Revenue                           \$252,000^a \$ 48,000 U \$300,000c

Variable costs          84,000^d    36,000 F   120,000f

Contribution margin   168,000 12,000 U  180,000

Fixed costs                   150,000     5,000 U 145,000

Operating income        \$18,000    \$ 17,000 U \$35,000

\$17,000 U

Total static-budget variance

b.

2. Prepare a flexible budget based variance analysis of the September performance

Flexible-              Sales

Actual    Budget        Flexible Volume          Static

Results Variances Budget Variances Budget

(1)           (2) = (1) – (3)   (3)         (4) = (3) – (5) (5)

Units sold         12,000         0      12,000     3,000 U 15,000

Revenue \$252,000a \$12,000 F   \$240,000b    \$60,000 U     \$300,000c

Variable costs   84,000  12,000F   96,000e   24,000 F   120,000f

Contribution margin 168,000 24,000 F 144,000 36,000 U 180,000

Fixed costs 150,000     5,000 U 145,000 0 145,000

Operating income \$18,000  \$19,000 F (\$1,000) \$36,000 U \$35,000

\$19,000 F                   \$36,000 U

Total flexible-budget        Total sales-volume

variance       variance

\$17,000 U

Total static-budget variance

The letters below represents

a 12,000 × \$21 = \$252,000   d 12,000 × \$7 = \$84,000

b 12,000 × \$20 = \$240,000   e 12,000 × \$8 = \$96,000

c 15,000 × \$20 = \$300,000   f 15,000 × \$8 = \$120,000

3.. flexible budget based variance analysis is an offshoot of static budget based variance analysis.Static budget will not be considered because there is a reduction in volume from 15000 t0 12000. Also flexible budget allows the management to make some changes as per assumptions while static budget is the same the changes from the assumption notwithstanding.

How do you spell gymnastics?