Homework Statement
Consider the equation
y0 = Ly; y(0) = 1:
**L = lamda**
Verify that the solution to this equation is y(t) = e^(Lt). We want to solve this equation numerically to obtain an approximation to y(1). Consider the two following methods to approximate
the solution to this...
|G| = g = mh = m(nk) = (mn)k. so that makes sense, but how do you relate that to the left cosets of K in G. or in other words, how do you relate that to the index of K in G. so does it suffice to state that a coset in H partitions H into |G| subsets? im just having difficulty seeing the...
Homework Statement
suppose that H and K are subgroups of a group G such that K is a proper subgroup of H which is a proper subgroup of G and suppose (H : K) and (G : H) are both finite. Then (G : K) is finite, and (G : K) = (G : H)(H : K).
**that is to say that the proof must hold for...
a set is open if every point in the set is an interior point. now i know that but i am having difficulty proving it.
(every point being an interior point that is)
my mistake
for the first one i meant to say write
the closure (interior A) is a proper subset of the interior (closure A)
i took A = [1,2]
then the right side would equal [1,2] and the left would be (1,2).
therefore
the (closure (interior A)) is not a proper subset of the...
im reading rudin's book: principles in mathematical analysis, ad we are talking about metric spaces, ie topology. so can you expand on you second approach to the problem please?
Homework Statement
6) Prove or give a counter-example of the following statements
(i) (interiorA)(closure) intersect interior(A(closure)):
(ii) interior(A(closure)) intersect (interiorA(closure)):
(iii) interior(A union B) = interiorA union interiorB:
(iv) interior(A intersect B) =...
If G and H are groups and f is a homomorphism from G to H, then the kernel K of f is a normal subgroup of G, the image of f is a subgroup of H, and the quotient group G /K is isomorphic to the image of f.
Homework Statement
can someone explain the 1st isomorphism theorem to me(in simple words) i really dont get it
Homework Equations
The Attempt at a Solution
Homework Statement
let R* be the group of nonzero real numbers under multiplication. then the determinant mapping A-> det(A) is a homomorphism from GL(2,R) to R*. the kernel of the determinant mapping is SL(2,R).
i am suppose to show that this is a homomorphism but i have no idea where to...