Recent content by indigogirl

I want to show that the integral from -1 to 1 of z^i = (1-i)(1+exp(-pi)/2 where the path of integration is any contour from z=-1 to z=1 that lies above the real axis (except for its endpoints). So, I know that z^i=exp(i log(z)) and the problem states that |z|>0, and arg(z) is between -pi/2...

Homework Statement 1. If X, Y, and Z have uniforj density of 1 on unit cube, then find P(X+Y+Z<1) 2. X1, X2, and X3 are independent and normal. Find distribution of Y=(X1^2+X2^2+X3^2)^(1/2) The Attempt at a Solution 1. I set up a triple integral, but I'm not sure if I got the limits...

Anyways, I found an easier, induction-less proof. U^(m+1)(V)=U^m(U(V)), and this subspace is included in U^m(V) If rank(U^m)=rank(U^m+1), then the above 'inclusion' turnsinto an equal sign. So, U^m(U(V))=U^m(V). Rewriting U(U^m(V))=U^m(V) This means that U can be applied to U^m(V) any...

Let me explain this better. Using what we're given, we have: rank(U^((m+n)+1)) = rank(U^(v+1)) for v=m+n rank(U^v)=rank(U^(m+n))=rank(U^m)=rank(U^m+1) but the last statement in no way implies that rank(U^m+1)=rank(U^v+1)=rank(U^v)

I don't think this proof works: You can't say, rank(U^((m+n)+1)) = rank(U^(v+1)) *v=m+n = rank(U^v) because what you're trying to PROVE is that rank(U^(v+1))=rank(U^v) It might be clearer to explain using numbers. Let m=3, then from the problem, rank(U^3)=rank(U^3+1)=rank(U^4). In the...

Linear algebra questions (rank, generalized eigenspaces) Hi, This seems to be an easy question on rank, but somehow I can't get it. Let U be a linear operator on a finite-dimensional vector space V. Prove: If rank(U^m)=rank(U^m+1) for some posiive integer m, then rank(U^m)=rank(U^k)...

Hi, In the isopentyl acetate synthesis from acetic acid and isopentyl alcohol, what do you extract it with? All the things I've read online say to extract with water, then 2x sodium bicarbonate, then saturated NaCl. However, the procedure we are supposed to modify this from is different. In...

Hi, I am having trouble with the question above. In general, I have trouble with questions like: What is the basis for all nxn matrices with trace 0? What is the dimension? What is the basis of all upper triangular nxn matrices? What is the dimension? Please help!