Recent content by hoopsmax25

Could you do a*b*b-inverse=b*b-inverse? and go from there?

I thought about using the inverse of b but I'm not sure how to plug it in?

Homework Statement If G is a group, a is in G, and a*b=b for some b in G (* is a certain operation), prove that a is the identity element of G Homework Equations The Attempt at a Solution I feel like you should assume a is not the identity element and eventually show that a= the...

Homework Statement p(x)=((x−1)^2 −2)^2 +3. From here find the full factorization of p(x) into the product of first order terms and identify all the complex roots. Homework Equations I am having trouble doing this by hand. I know there are four complex roots but can't seem to figure out...

Yeah and i understand that but we are asked to prove it, not explain why.

Homework Statement Suppose a, b ∈ N and a|b. Prove that a = gcd(a, b). Homework Equations Seems easy intuitively but actually proving it is giving me problems. The Attempt at a Solution I have been trying to use the fact that gcd(a,b)=na + mb here m and n are integeres but got stuck.

Oh ok, so obviously it cannot. So is there a way to show that the contradiction by writing it out?

yeah i understand that. i think that's where i am stuck at. i don't know what the next step would be.

Homework Statement Show that there is no vector ⃗e that has the property of the number 1 for cross product, namely that ⃗e × ⃗x = ⃗x for all ⃗x. Homework Equations I'm sort of stuck on how to show this. The Attempt at a Solution I set e=(e1,e2,e3) and x=(x1,x2,x3) and used cross...

Awesome. Thanks for the help

Ok i get that now. So if d(t)=1, which is a constant, then d(t) dotted with d'(t) =0. Since c(t)/||c(t)|| has the same direction as c(t), we can then plug c(t) in for d(t). Does that make sense to do?

would it be 1?

Homework Statement Let c(t) be a path of class C1. Suppose that ||c(t)||>0 for all t. Show that c(t) dot product with d/dt((c(t))/||c(t)||) =0 for every t. Homework Equations I am having trouble with the derivative of (c(t)/||c(t)||) and how to show that when its dotted with c(t) that...