if l = P + [v] =Q +[w], how must P, Q, v and w be related? note that l= P+[v] be a line with unit vector v then, [v] is called the span of v, l is a line, P is a point , Q is a point, and [w] is called the span of w Solution Given l=P+[v] is a line where [v] is a span of a unit vector v, we can write [v]=cv, c is a scalar which spans v. when c=0, we get P+[v] =P+cv=P+0=P. i.e the point P lies on a line l. Similarly l=Q+[w] is a line where [w] is a span of a vector w, we can write [w]=kw, k is a scalar which spans w. when k=0, we get Q+[w] =Q+kw=Q+0=Q. i.e the point Q lies on a line l. From these two points, we understood that the points P and Q lies on the line l. i.e Q=P+nv; n is a scalar. since P and Q are on same line l, we can say that [v] and [w] are same by saying that directions of v and w are same but magnitudes may be different. Since the directions of v and w are same, we can write the vector w is a scalar combination of unit vector v, i.e w=dv, where d is a scalar such that ||w||=|d|. Finally we can write Q+[w]=(P+nv)+kw = (P+nv)+kdv = P + (n+kd)v = P + [v], both represents the same line l..

1. Impact of Government Events
Indicate how each of the following transactions impacts the fund balance of the general fund for
fund-based financial statements, and what the impact is on the net asses balance for the
governmental finds for government-wide financial statements.
Fund A transfers $20,000 to Fund B. For each of the following, indicate whether the statement is
true or false and, if false, explain why.
a.If Fund A is the general fund and Fund B is an enterprise fund, nothing will be shown for this
transfer on the statement of activities within the government-wide financial statements.
b.If Fund A is the general fund and Fund B is a debt service fund, nothing will be shown for this
transfer on the statement of activities within the government-wide financial statements.
c.If Fund A is the general fund and Fund B is an enterprise fund, a $20,000 reduction will be
reported on the statement of revenues, expenditures, and other changes in fund balance for the
governmental funds within the fund financial statements.
d.If Fund A is the general fund and Fund B is a special revenue fund (which is not considered a
major fund), no changes will be shown on the statement of revenues, expenditures, and other
changes in fund balance within the fund financial statements.
e.If Fund A is the general fund and Fund B is an internal service fund and this is for work done,
the general fund will report an expense of $20,000 within the fund financial statements.
Solution
A .False - A transfer out will be shown by the governmental activities. Transfer in will be
reported by the business type activities. No overall mpact s shown in the total column for the
government as a whole. But both figures do appear in their own seperate columns.
B. This is an intra activity transfer. Funds within the governmental activities are involved, this
transfer creates no difference in the overall toal.
C. True The General Fund reports the resource outflow as on other financig use. Financial
resources were reduced but it was not for an expenditure.
D. False The general fund will report the transfer out as an other financing use. All othr Funds
coloumn will sshow the transfer in as an other financing source.
E. False. The General fun d does not report expenses in the fund.based financial statements but
rather expenditures.