Recent content by margaret37

Thank you very much. I think the light MAY be starting to dawn.

I do see the difference. (Which is not how it is written on my assignment.) So does K operate on x? Are t and s scalars? So for a trivial example... \int {e^{nx}} = ne^nx So is this a solution to some integral equation similar to the problem? Thank you for your answer

Oops. :( But is this the right way to do it?

Homework Statement Find all non-zero eignvalues and eigenvectors for the following integral operator Kx := \int^{\ell}_0 (t-s)x(s) ds in C[0,\ell] Homework Equations \lambda x= Kx The Attempt at a Solution \int^{\ell}_0 (t-s)x(s) ds = \lambda * x(t)...

Thank you for answering, unfortunately I'm still confused. Why wouldn't it be closed? If I set up a sequence within S, wouldn't it necessarily converge to something also inside S.

Homework Statement Prove that for a linear set M a subset of Hilbert space, that the set perpendicular to the set perpendicular to M is equal to M iff M is closed. The Attempt at a Solution I already have my proof -- but what is an example of a linear subset of H that is not closed? I think...

Thanks

Thanks, I believe I understand. I said it backwards ... S is closed and bounded on the Reals so it is compact. The union of the open intervals U = (-1, 1-1/n) for all positive n, covers S. That is, S is a subset of U. But if one takes a finite subset of u, then the finite union F...

Homework Statement Show that S = [0,1) is not compact by giving an closed cover of S that has no finite subcover. Homework Equations The Attempt at a Solution I know that S is not compact because it is an open not a closed set even though it is bounded. But I am completely...

Thank you very much. I think I've got it now.

You're pretty close Magnitude = sqrt(deltaX^2 + deltaX^2) <> 2 And you want the vector going in the direction that would get you from a to b. So you want to subtract b-a to get the direction

Homework Statement Define T : R3x1 to R3x1 by T = (x1, x2,x3)T = (x1, x1+x2, x1+x2+x3)T 1 Show that T is a linear transformation 2 Find [T] the matrix of T relative to the standard basis. 3 Find the matrix [T]' relative to the basis B' = {(1,0,0)t, (1,1,0)t, (1,1,1)t 4 Find the...