Sean and Shannon Fleming are partners in a business called CarpetClean. Journals and forms for completing this problem are given in the Working Papers. CarpetClean completed the following transactions during the current year.

The Flemings decided to liquidate CarpetClean and retire on December 31. On that date, after financial statements were prepared and closing entries were posted, the general ledger accounts had the following balances:

Cash                                            $108,980.00 
Merchandise Inventory                              4,000.00
Equipment                                         30,000.00
Accumulated Depreciation-Equipment                20,000.00
Accounts Payable                                   5,000.00
Sean Fleming, Capital                             60,620.00
Shannon Fleming, Capital                          57,360.00

The following transactions occurred on December 31 of the current year:

Transactions:

a. Received cash from the sale of merchandise inventory,$3,600.00. R345.
b. Received cash from the sale of equipment, $14,000.00. R346.
c. Paid cash to all creditors for amounts owed. C575.
d. Distributed balance of Gain on Realization to the partners on an equal basis. M288.
e. Distributed balance of Loss on Realization to the partners on an equal basis. M289.
f. Distributed remaining cash to partners. C576 and C577.

5. Journalize the transactions. Continue on the next available line of the journals.

Suppose $T \in \mathcal{L}(V)$ and $v_{1}, \dots, v_{n}$ is a basis of V that is a Jordan basis for T. Describe the matrix of $T^{2}$ with respect to this basis.

Let W be a subspace of a finite-dimensional vector space V, and consider the basis

$$\{u_1,u_2,... ,u_k\}$$

for W. Let

$$\{u_1,u_2,... ,u_k,u_{k+1},... ,u_n\}$$

be an extension of this basis to a basis for V. Prove that

$$\{u_{k+1} + W, u_{k+1}+ W , . . . , u_n + W\}$$

is a basis for V/W. Let W be a subspace of a finite-dimensional vector space V, and consider the basis

$$\{u_1,u_2,... ,u_k\}$$

for W. Let

$$\{u_1,u_2,... ,u_k,u_{k+1},... ,u_n\}$$

be an extension of this basis to a basis for V. Derive a formula relating dim(V), dim(W), and dim(V/W).

Fio Barellis was discussing summer employment with Sara Rida, president of Xanadu Construction Service:
Sara: I’m glad that you’re thinking about joining us for the summer. We could certainly use the help.
Fio: Sounds good. I enjoy outdoor work, and I could use the money to help with next year’s school expenses.
Sara: I’ve got a plan that can help you out on that. As you know, I’ll pay you $\$12$ per hour, but in addition, I’d like to pay you with cash. Since you’re only working for the summer, it really doesn’t make sense for me to go to the trouble of formally putting you on our payroll system. In fact, I do some jobs for my clients on a strictly cash basis, so it would be easy to just pay you that way.
Fio: Well, that’s a bit unusual, but I guess money is money.
Sara: Yeah, not only that, it’s tax-free!
Fio: What do you mean?
Sara: Didn’t you know? Any money that you receive in cash is not reported to the IRS on a W-$2$ form; therefore, the IRS doesn’t know about the income—hence, it’s the same as tax-free earnings.
$\blacktriangleright$ How should Fio respond to Sara’s suggestion?

For differential equation $y''-4y'=0$ give a basis and a solution space in term of basis.

Let

$$V = M _ { 3 } ( \mathbb { R } )$$

and let S be the subset of all vectors in V such that the sum of the entries in each column is zero. (a) Find a basis and the dimension of S. (b) Extend the basis in (a) to a basis for V.

Marvin Turner was discussing summer employment with Tina Song, president of Motown Construction Service:

Tina: I’m glad that you’re thinking about joining us for the summer. We could certainly use the help.

Marvin: Sounds good. I enjoy outdoor work, and I could use the money to help with next year’s school expenses.

Tina: I’ve got a plan that can help you out on that. As you know, I’ll pay you $14 per hour, but in addition, I’d like to pay you with cash. Since you’re only working for the summer, it really doesn’t make sense for me to go to the trouble of formally putting you on our payroll system. In fact, I do some jobs for my clients on a strictly cash basis, so it would be easy to just pay you that way.

Marvin: Well, that’s a bit unusual, but I guess money is money.

Tina: Yeah, not only that, it’s tax-free!

Marvin: What do you mean?

Tina: Didn’t you know? Any money that you receive in cash is not reported to the IRS on a W-2 form; therefore, the IRS doesn’t know about the income—hence, it’s the same as tax-free earnings.

b. How should Marvin respond to Tina’s suggestion?

For differential equation $y''-10y'+25y=0$ give a basis and a solution space in term of basis.

If G is free abelian with basis {x, y}, show that $\{2 x+3 y, x-y\}$ is also a basis for G.

Find a basis for the space of polynomials p(x) of degree ≤ 3. Find a basis for the subspace with p(1) = 0.

Daryl Kirby opened Squid Realty Co. on January 1, 2013. At the end of the first year, the business needed additional capital. On behalf of Squid Realty Co., Daryl applied to Ocean National Bank for a loan worth $375,000. Based on Squid Realty Co.’s financial statements, which had been prepared on a cash basis, the Ocean National Bank loan officer rejected the loan as too risky.

After receiving the rejection notice, Daryl instructed his accountant to prepare the financial statements on an accrual basis. These statements included$65,000 in accounts receivable and $25,000 in accounts payable. Daryl then instructed his accountant to record an additional$30,000 of accounts receivable for commissions on property for which a contract had been signed on December 28, 2013. The title to the property is to transfer on January 5, 2014, when an attorney formally records the transfer of the property to the buyer.

Daryl then applied for a $375,000 loan from Free Spirit Bank, using the revised financial statements. On this application, Daryl indicated that he had not previously been rejected for credit.

Discuss the ethical and professional conduct of Daryl Kirby in applying for the loan from Free Spirit Bank.

Give the standard basis for $\mathrm{R}^4$.

(a) Show that the vectors in the basis span $\mathrm{R}^4$.

(b) Show that the vectors in the basis are linearly independent.

Give the standard basis for $\mathrm{R}^2$.

(a) Show that the vectors in the basis span $\mathrm{R}^2$.

(b) Show that the vectors in the basis are linearly independent.

Prepare a statement of cash flows for Travel Lite Corporation using the direct method. Use the balance sheet from the previous exercise and the information below. A form is given in the Working Papers.

Prepare a statement of cash flows for the current year.

Cash balance at the beginning of the period     $39,522.51 
Cash receipts during the year:
    Cash from sales$598,236.31 
    Cash from interest                               635.21 
    Cash from rent                                 4,000.00 
    Cash from sale of equipment                    1,200.00
    Cash from issuance of stock                   17,500.00
    Cash from issuance of bonds                   10,000.00
Cash payments during the year:
    Cash for inventory                          $375,623.54 
    Cash for salaries and wages                   85,807.14 
    Cash for insurance                             4,254.35 
    Cash for interest                              1,587.35 
    Cash for taxes                                12,885.00
    Cash for rent                                 16,248.65 
    Cash for other operating expenses             95,412.88 
    Cash for purchase of equipment                10,549.00 
    Cash for payment of notes payable              2,500.00    
    Cash for payment of dividends                 21,200.00