Question
In: Advanced Math
(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...
(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three elements. Calling the elements a, b, c, exhibit, for each of these matroids, its bases, cycles and independent sets.
(b) Consider the matroid M on the set E = {a, b, c, d}, where the bases are the subsets of E having precisely two elements. Detrmine all the cycles of M, and show that there is no graph G such that M is the cycle matroid M(G).
Solutions
Colby Messinger answered 1 year agoRelated Solutions
(a) Show that there are, up to isomorphism, exactly 8 matroids whose underlying set has three...
(a) Show that there are, up to isomorphism, exactly 8 matroids
whose underlying set has three elements. Calling the elements
a,b,c, exhibit, for each of these matroids, its bases, cycles and
independent sets.
(b) Consider the matroid M on the set E = {a,b,c,d}, where the
bases are the subsets of E having precisely two elements. Detrmine
all the cycles of M, and show that there is no graph G such that M
is the cycle matroid M(G).
show thar up to isomorphism there are two abelian groups of order 200that have exactly 7...
show thar up to isomorphism there are two abelian groups of order
200that have exactly 7 subgroups of order 2
using theorem 11.10 (First Isomorphism Theorem), Show that the set of positive real numbers with multiplication...
using theorem 11.10 (First Isomorphism Theorem), Show that the
set of positive real numbers with multiplication is isomorphic to
the set of real numbers with addition.
Theorem 11.10 First Isomorphism Theorem. If ψ : G → H is a group
homomorphism with K = kerψ, then K is normal in G. Let ϕ : G → G/K
be the canonical homomorphism. Then there exists a unique
isomorphism η : G/K → ψ(G) such that ψ = ηϕ.
Using only real numbers between 0 and 100, inclusive, show the set of three numbers whose...
Using only real numbers between 0 and 100, inclusive, show the
set of three numbers whose product is 64 and whose sum is minimal
is give by {4, 4, 4}.
(a) When is an absolute minimum or maximum guaranteed?
(b) State the steps to find an absolute minimum and maximum.
(c) Is the space closed and bounded? Explain.
(d) Use Lagrange Multipliers to find the minimum and maximum
please label and write neatly.
An amusement park, whose customer set is made up of two markets, adults and children, has...
An amusement park, whose customer set is made up of two
markets, adults and children, has developed demand schedules as
follows:
Qa = 20 – Pa
where a is adult market
Qc = 30 – 2
Pc Where c is
children market
QT = 50 – 3 PT
where T is the two markets combined
Assume that the marginal cost of each unit of quantity
is $5 (constant), the owners of the park want to maximize...
An amusement park, whose customer set is made up of two markets, adult and children, has...
An amusement park, whose customer set is made up of two
markets, adult and children, has developed demand schedules as
follows:
Price ($)
Quantity, Adults
Quantity, Children
5
15
20
6
14
18
7
13
16
8
12
14
9
11
12
10
10
10
11
9
8
12
8
6
13
7
4
14
6
2
The marginal operating cost of each
unit of quantity is $5. (Hint: Because marginal cost is a constant,
so is average variable cost....
An amusement park, whose customer set is made up of two markets, adults and children, has...
An amusement park, whose customer set is made up of two markets,
adults and children, has developed demand schedules as follows:
Price ($) Quantity Adults Children 5 15 20 6 14 18 7 13 16 8 12 14
9 11 12 10 10 10 11 9 8 12 8 6 13 7 4 14 6 2 The marginal operating
cost of each unit of quantity is $5. Because marginal cost is a
constant, so is average variable cost. Ignore fixed...
An amusement park, whose customer set is made up of two markets, adults and children, has...
An amusement park, whose customer set is made up of two
markets, adults and children, has developed demand schedules as
follows:
Qa
= 20 –
Pa where
a is adult market
Qc
= 30 – 2
Pc Where c is
children market
QT
= 50 – 3
PT where T is
the two markets combined
Assume that the marginal cost of each unit of quantity
is $5 (constant), the owners of the park want to maximize
profit:
Calculate the price, quantity and profit...
An amusement park, whose customer set is made up of two markets, adults and children, has...
An amusement park, whose customer set is made up of two markets,
adults and children, has developed demand schedules as follows: Qa
= 20 – Pa where a is adult market Qc = 30 – 2 Pc Where c is
children market QT = 50 – 3 PT where T is the two markets combined
Assume that the marginal cost of each unit of quantity is $5
(constant), the owners of the park want to maximize profit: A)
Calculate the...
Use a three-period CRR binomial model (meaning three jumps total up or down in the underlying)...
Use a three-period CRR binomial model (meaning three jumps total
up or
down in the underlying) to price a European call option for a
stock whose
share price today is S = 16 when the interest rate is r = 4%,
the maturity
date is 6 months (so T = .5 in years), the strike price is K =
17.5 and the
volatility is ? = 20% = .2. ,u=e(?*sqrt(T/N)).
d=e(-?*sqrt(T/N))
Using put-call parity, price a corresponding put option as...
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