Let U and V be vector spaces, and let L(V,U) be the set of all
linear transformations from V to U. Let T_1 and T_2 be in
L(V,U),v be in V, and x a real number. Define
vector addition in L(V,U) by
(T_1+T_2)(v)=T_1(v)+T_2(v)
, and define scalar multiplication of linear maps as
(xT)(v)=xT(v). Show that under
these operations, L(V,U) is a vector space.
Let u and v be two integers and let us assume u^2 + uv +v^2 is
divisible by 9. Show that then u and v are divisible by 3. (please
do this by contrapositive).
. Let U be a non-empty set. For A and B subsets of U, define the
relation A R B if an only if A is a proper subest of B. a. Is R
reflexive? Prove or explain why not. b. Is R symmetric? Prove or
explain why not c. Is R transitive? Prove or explain why not. d. Is
R antisymmetric? Prove or explain why not. e. Is R an equivalence
relation? Prove or explain why no
(a) Let U(A,B) = (A)^1/3 (B)^2/3 , where A and B are two
distinct consumption goods. Compute the marginal utility for A,
MU_A and the marginal utility for B, MU_B. Provide an
interpretation for what these mean.
(b) Compute the marginal rate of substitution (MRS) for a
consumer given the preference given in part (a).
(c) Provide an interpretation for what the MRS means.
(d) Explain why at the point (A, B) that maximizes a consumer’s
utility function U(A, B)...
Given a second order process: 2 AB → A 2 + B 2 with k = 0.0908
M-1min-1; and the initial concentration of AB = 0.941 M, calculate
the concentration of A2 after exactly 20 min. Enter the result with
3 sig. figs. exponential notation and no units.