1:Mp.q(C) is the vector space of all px q complex matrices over C. (recall that this means the "vectors" in this vector space are actually matrices). Let tr(A) denote the trace of a square matrix A. (a) Show that (A, B) = tr(A"B) makes sense and establishes an inner product on Mp.q for A, B, and Mpq(C) (C). (c) Allow Mpq (C). Let Z1 = u,v" and write its SVD A = UEV" with u and v signifying the ith columns of U and V, respectively. Show that Z1,..., Z, is an orthonormal set in this inner product by setting r = minp, q). (c) Let = span (Z1,..., Z,,,,,,,,,,,,,,,,,,,,,,,,,,, In the basis (Z1,..., Z,) of 7, what are A's coordinates?

2:L. Frank Baum remarked in The Wonderful Wizard of $mathrmO z$ and other books about the Land of $mathrmO z$ that most products would not be rare if people's wants were constrained sufficiently. This was the case in Oz, according to Baum: "There were no poor people in the Land of Oz since there was no such thing as money." Each person was provided whatever he required for his usage by his neighbors, which was as much as anyone could reasonably wish. Some tilled the ground and grew large amounts of grain, which were distributed evenly among the entire population, ensuring that everyone had enough. There were many tailors, dressmakers, shoemakers, and other artisans who created clothing for anyone who wanted it. Similarly, jewelers created ornaments for persons that pleased and beautified them, and these ornaments were also given out to those who requested for them. The neighbors provided food, clothing, a home, furniture, ornaments, and games to each man and woman, regardless of what they contributed for the good of the community. If the supply ever ran out, more was taken from the Ruler's vast storehouses, which were then replenished when there was more of any item than people need... As you can see from everything I've said so far, the Land of Oz was a fascinating country. With us, I don't think such an agreement would be feasible. Do you agree with Baum that the economic system in Oz would not work in today's America? Explain why or why not in a few sentences.

3:1a.Dominic has been a long-time client of yours. You analyze Maria's retirement portfolio performance and confirm that she is making progress as planned during your quarterly discussion with her. Which step of the financial planning process are you currently working on?

A. Tracking and updating progress.

B. Gaining an understanding of the client's personal and financial situation

C. Making Recommendations for Financial Planning

D. Putting the Financial Planning Recommendations into Practice.

1b. All of the following are examples of qualitative data that the financial planner should acquire EXCEPT:

Aims of education

B. Tolerance for risk

C. Age and number of children of the client

D. Spending mentality in general

1c. In a disability policy, the time between the onset of benefits under the contract and the onset of benefits is referred to as the:

A. Disabled for a certain amount of time.

B. Period of Elimination

Discount Period (C).

D. The Waiting Period

1d. On a statement of net worth, which of the following transactions is most likely to appear? (4-61)

All of the aforementioned.

Other than cash, you can inherit property.

Contributions to a retirement savings account made by the employer.

The increase in the value of a primary residence.