Prove that the field Q(√2,√3,u) where u^2=(9-5√3)(2√2) is normal over Q.
I'm supposed to show that this field is the splitting field of some polynomial over Q. u is clearly algebraic over Q. Do i just take the higher powers of u and try to find the minimal polynomial over Q or is there a...
G, H, K are groups. G is finite. GxH is isomorphic to GxK. Prove H is isomorphic to K. Give an example to show that this does not hold when G is infinite.
The counter example when G is infinite is Rx{0} and RxR (R - real numbers)
I'm having trouble Proving the main part of the question. I...
Statement: V is a finite dimensional vector space with basis {ei} (i goes from 1 to n). V has a norm || || defined on it(not necessarily induced by an inner product). Let x=Ʃxiei belong to V. I want to show that ||x|| ≥ ||xiei|| for any fixed i.
I'm not entirely sure this result is correct...
Your proof is a little hard to read. In your proof you seem to have proved ab=e for all a,b in G? that looks fishy...
this is a solution. https://www.physicsforums.com/showthread.php?t=529381
A matrix is invertible if and only if it has non-zero determinant. What can you say about the determinant of a nilpotent matrix?
C. You could prove this by assuming it is false i.e. I-A is not invertible and then proceeding.
Reflexive means a~a. Can you find an element in H and another in K such that a=h.a.k?
Symmetric means a~b => b~a. So if a=h.b.k, you need to show b=h'.a.k' for some h' in H and k' in K.
Just use the definitions...
Where did your x come from?
Cauchy means for all r>0, there exists a natural number p such that for all m,n>p, d(x_m,x_n) < r.
In this case, max{|xn(1)-xm(1)|,|xn(2)-xm(2)|}<r for all n,m>p