ha

int_{0} ^{a} sqrt( a^2 -x^2) dx

thank you very much.

Given S is a sebset of R^n? I have to prove that the affine hull of S is the smallest affine space containing S.

You dont have to give me the full proof, some golden hints are good enough.

I appreciate all your helps,

Ha

I do know the answer but I can't figure out what the intermediate steps are.

sum_(k=1)^infinity k/ [(r+1)^k ] = (r+1)/r^2

Please help!

Ha

Just give me some hints, you don't have to give the full proof. Any help is appreciated.

Ha

Do anyone know where I can get the solution for excersises in the book Graph Theory with Applications from J.A.Bondy and U.S.R. Murty

thank you very much ;D

The whole sentence:

" After switching on the fan the load dump resistance is

tested. This resistance is used when the grid goes down. In that case it is prohibited

to deliver electricity to the grid. The generated electricity at that time will go to

the load dump resistance."

Thanx very much :D

p(x) = 1+x+x^3+x^4+x^5 an element from Z2[x] (Z modulo 2 [x])

I have shown that p(x) is irreducible, so F= Z2[x]/ (p(x)) is a field

I think F has 2^5 elements, am I right?

K is a field with dimension d, you can see it as a vector space over Z2, and Z2 subset of K subset of F.

I think K has 2^d elments, but I'm not sure.

If you see F as a vector space over K, what is the dimension of F then?

How can I conclude K= Z2 or K=F

thanx :)

first I have to show that p(x)= x^4+x+2 is irreducible overZ3( Z modulo 3)

I know how to do it for polynomials with degree two or three but p(x) has degree 4.

then F= Z3 [x] /<p(x)> is a field, now I guess {x^3, x^2, x, 1} is a basic but the four vectors seems linear dependent ???

U(10)= {1,3,7,9} (the binaire opertion is multiply modulo 10)

U(12)={1,7,9,11} (the binaire opertion is multiply modulo 12)

Are these groups isomorph?

Thanx

V is the space of all the infintely differentiable functions f: [0,1] -> C (C the complex numbers)

with f(0)= f(1) = 0.

W is a subspace of V, W= all polynom with degree less or equals 3.

Find a basic for W

thanx !!!

I have to construct a space V (not a vector space) over field F(not necessary R or C).

So I have the freedom to define the sum of two vectors v + w

and the scalar product a.v and field F.

V must satisfy at least 6 of the next 8 axioms (for vector space) but not all (V is not a vector space).

Axioms

u + (v + w) = (u + v) + w.

v + w = w + v.

There exists an element 0 ∈ V, such that v + 0 = v for all v ∈ V.

For all v ∈ V, there exists an element w ∈ V, such that v + w = 0.

a(v + w) = av + aw

(a + b)v = av + bv

a(bv) = (ab)v

1v = v, where 1 denotes the multiplicative identity in F.

Thank u ^^

I have to construct a space V (not a vector space) over field F(not necessary R or C).

So I have the freedom to define the sum of two vectors v + w

and the scalar product a.v and field F.

V must satisfy at least 6 of the next 8 axioms (for vector space) but not all (V is not a vector space).

Axioms

u + (v + w) = (u + v) + w.

v + w = w + v.

There exists an element 0 ∈ V, such that v + 0 = v for all v ∈ V.

For all v ∈ V, there exists an element w ∈ V, such that v + w = 0.

a(v + w) = av + aw

(a + b)v = av + bv

a(bv) = (ab)v

1v = v, where 1 denotes the multiplicative identity in F.

Thank u ^^

What is var(X-Y)

I know that var (X+Y) = var(X) + var (Y) + cov (X,Y)

Can anyone help me to solve this:

int(x^2 * exp^[-(1/2)*x^2], x = -infinity .. infinity)

I know the answer is sqrt(2*Pi)

but I dont know how to get it

Can someone explain me why the determinant is the product of all eigenvalues?

thanx,

:D

why is

limit for k-> infinity [k/(k+1)]^k =1/e???

tHanX

why is

limit for k-> infinity [k/(k+1)]^k =1/e???

tHanX

S5 is the group permutation of {1,2,3,4,5}

a. Find a permutation of order 6 in S5?

b. H and G are subgroups of S5. The order of H is 8 (H has 8 elements), the order of G is 15. How many elements does (H intersect G) has?

Thanks a lot

PS: question b I know that de identity element is in H and in G but I dunno what about the other seven element of H.

Suppose that an experiment can result in one of r possible outcomes, the i-th outcome having probability pi (i=1,2..,r) en sum from i=1 to r of pi =1.

n of these experiment are performed, and if the outcome of the n does not affect the outcome of the n- 1.

let Ni denote the number of times outcome i occur.

Find

Cov(Ni,Nj ) en compute the expected number of outcomes that do not occur

Ps: I have computed E(Ni) = npi

Var (Ni) = npi (1-pi)

I got the hint from the teacher that N1+N2+...+Nr = n (a constant)

so Var (N1+ N2+..+Nr) = 0

I really appreciate your help

me