Recent content by SMC

ok, I looked over the posts after having had time to clear my mind and I'm pretty sure I get it now. thank you very much for your help!

yes but I already did that, I solved the system as you can see above I found x1 and x2 in terms of x3 and x4 but then the solution says that the matrices that make up the basis are \begin{bmatrix}12 & -9 \\ 4 & 0 \end{bmatrix} and \begin{bmatrix}1 & 0 \\ 0 & 1 \end{bmatrix} I just don't...

in the R4 case you just take the rows that remain in the matrix after the reduction and those are the vectors that make up the basis right? but in the R2,2 case the basis is made up of matrices instead of regular vectors so you go through the same procedure but then how do you know what matrix...

Homework Statement i know how to find the basis of a subspace of R2 or R3 but I can't figure out how to find the basis of a subspace of something like R2,2. I even have an example in my book which i managed to follow nearly till the end but not quite... Given matrix: A= 6 -9 4 -4 show that...

i considered e^0 = 0 I've made this mistake quite a few times especially in integrlas! o0)

OMG I just realized what I did! I'm really sorry! never mind! please ignore!

i just did the integral 0 and 10 of the function given and put it equal to 1 because the probability of it failing within a 10 year period is 100%. once I've done the integral I get: 10 - k*e^(-10/t0)*(-t0) = 1 (int. between 0 and 10 of 1 is 10 and int. between 0 and 10 of k*e^(-t/t0) is...

yeah sorry that t should be tmax = 10... I've edited it

Homework Statement The technical specification of a particular electrical product states that the probability of its failure with time is given by the function: f(t) = 1 - ke^(-t/t0) if 0 < t < tmax f(t) = 0 if t > tmax where t is the time of service...

well i know constantan is an alloy of copper and nickel which I guess have fairly small nuclei which which increases scattering time and decreases resistivity. I'm not sure I fully understood what you're asking though

Homework Statement For some applications it is important to minimize the temperature dependence of electronic components. For example, there is a special alloy called constantan that can be used for temperature independent resistance elements. Do you expect constantan to have a high or low...

so this is the question I'm having a little trouble with: Assume that the ratio of copper resistivity at room and absolute zero temperatures (so called "residual resistance ratio") is 1000. Estimate the electron mean free path in copper at low temperatures. we also know this: Let us assume...

yes ok that makes sense I should of noticed that, thank you Oxvillan. but I still don't understand why it asks me to derive fermi energy before wavenumber. is there a way of deriving fermi energy without deriving wavenumber first? or maybe the questions are just in the wrong order

Homework Statement Hello, I am preparing a condensed matter exam and I was wondering if I could get some help on the following question from a past exam paper: Show that for the free electron gas at zero temperature the Fermi energy is given by: ε_{F}=\frac{\hbar^{2}}{2m}(3π^{2}N)^{2/3} and...