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...
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...
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).
the (closure (interior A)) is not a proper subset of the...
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.
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...