Recent content by flash

Thanks for the help guys, I've got it now :)

Hi, I'm wondering if there is an exact solution to: (2t+1)e^{-2t}=5 I've tried and have been unable to solve this for t. I can get an approximate numerical answer using the calculator but that's it. Cheers

Thanks :-)

If I take F(x)=\sqrt{1+x^2}, then the derivative is always less than one so this is a contraction mapping from R to R, right? But there is no fixed point where F(x)=x, where the contraction mapping theorem says there should be. So where have I gone wrong? Cheers

Homework Statement When considering conservation of energy and momentum in the collision between a photon and an electron (in Compton scattering for example), is it reasonable to worry about 'stationary' electrons? The Attempt at a Solution From what I can recall the derivation of the...

Excellent, thanks a lot.

Hi, The problem is to determine whether or not relativistic effects are relevant for an electron accelerated to an energy of a) 100MeV and b) 100GeV. So I need to find the gamma factor of the electron in each of these cases. I have used E = \gamma m_0 c^2 and solved for gamma = 195 in the...

Thanks, that's what I wanted to know. Cheers

I would like to solve 2^k = \frac{n}{k} for k in terms of n, but can't seem to do it. Any help greatly appreciated!

Thanks. So do you mean: view the transformation associated with matrix A in a basis of {eigenvector, orthogonal to eigenvector} and find the matrix for the transformation in this basis? I'm not sure what the significance of the orthogonal vector is here.

Homework Statement Let A be a 2x2 real matrix which cannot be diagonalized by any matrix P (real or complex). Prove there is an invertible real 2x2 matrix P such that P^{-1}AP = \left( \begin{array}{cc} \lambda & 1 \\ 0 & \lambda \end{array} \right) I know how to diagonalize a matrix...

An acid solution flows at a constant rate of 6L/min into a tank which initially holds 200L of a 0.5% acid solution. The solution in the tank is kept well mixed and flows out of the tank at 8L/min. If the solution entering the tank is 20% acid then determine the volume of acid in the tank after t...

Ok, thanks. The other part of the question goes: A is a 4x3 matrix C is a 3x4 matrix such that CA = I Suppose, for some given b in R4 that Ax=b has at least one solution. Show that this solution is unique. Can I just say x = Cb which implies that there is only one solution for x? I'm thinking...

Ax = b CAx = Cb Ix = Cb x = Cb Am I on the right track?

Suppose A is a 3 x 4 matrix and there exists a 4 x 3 matrix C such that AC = I (the 3x3 identity matrix). Let b be an arbitrary vector in R3. Produce a solution of Ax=b. I'm not quite sure what the question is asking. I think I just need someone to point me in the right direction. Thanks