Recent content by brmath

I recently wrote that 25 is divisible by 3. And just a few months ago based a proof on the non-fact that 10 is prime. Talk about embarrassed. Losing a factor of 4 is much more understandable. We cannot escape these boneheaded errors.

You started out well. I think you made an arithmetic mistake when you multiplied your expression through by .5 -- you got ##e^{2u}/8 + e^{-2u}/8 +2u##. Where did you get 2u. Shouldn't it be u/4?

Here is a way to tackle your last question. The statement is true if A is diagonal. Can you show it is true if A is diagonalizable? Can you show it is true if A is not diagonalizable but is in Jordan form? I believe if A is in Jordan form with blocks ##J_1, J_2 ... ## etc then ##e^A## is...

Sorry I misunderstood. It was not entirely clear and I do not guess well. But the "magnitude" of the vector is its length isn't it? And the sides are defined to be of length 1. Thus I still do not understand the question. However, I'm glad you solved it.

It could be that your calculator is not set up to produce function like derivatives such as 2x, and will only produce a list of values on the curve of the derivative. Or it could be that there is a mode in which to do what you want, and you have to switch to it. Might I suggest you use...

My guess is that by compute he means to compute the vector length from the origin to the various points on the hexagon. To do this you need a way of representing each point P on the perimeter of the hexagon. That representation will depend on the angle between the origin and P. It is...

A very sensible message. I wonder how many of them took your advice.

Yes, students who are totally unprepared for the classes they are in are a problem. It should be the school's problem, but it winds up in our laps when the student asks for help. It is hard to know what to tell them. "Drop this class and study h.s. algebra" does not seem appropriate, although...

It does, but I think the a,b,c,d create a lot of complications.

The eigenvectors present a different kind of problem, and there are a number of different possibilities. I suggest you start by finding the eigenvectors of B which match the 0 eigenvalues: i.e. Bx = 0. You will get either one or two different x's. I suspect just one. With the A there are...

Will try to get back to you later today.

I can't figure out where the 1/4 came from.

Do read Dick's comments. I don't think what you are doing properly shows that you have a basis. In particular, you cannot assume that the a,b,c,d for the first equation are the same as for the second. What you want to show is that any set of coefficients, say ##\alpha, \beta, \gamma ##,η...

First, I'm not sure what the definition is of U + V. You seem to be implying that it is the space of the sums of the polynomials in U and V. Is that correct? We do need a definition. If so, I don't understand what 4x4 matrix you have extracted. Could you explain? Nor do I see where you...

If you place a problem in this homework section, you are supposed to follow the homework format. Can you please do that. As jedishrfu says, your problem is not correctly stated. If you are looking at ##\int xdx## that is easily solved. If by df(x) you mean f'(x), you should write it as...