Recent content by Essnov

I am hoping someone can help me with the following problem: Define f by: f(x, y) = 0 \ if \ (x, y) = (0,0) \ and \ f(x, y) = \frac{xy^{2}}{(x^{2}+y^{4})^{1/2}} \ otherwise The problem is to determine (and prove) whether the function is differentiable everywhere. First of all, the partials...

The point is that for any vector you should be able to come up with a linear combination of the coefficients to generate it. Here, your coefficient matrix reduces to a rank 3 matrix, so your 4 vectors span a 3 dimensional space in P3. P3 is a 4 dimensional vector space and so there are...

For a, you have to know that complex eigenvalues come in conjugate pairs. That is, if a + bi is an eigenvalue of a matrix A, then so is a - bi. The same goes for eigenvectors. If an eigenvector has entries (a, b + ci) then there is another eigenvector with entries (a, b - ci). For b, you have...

Thank you very much for your help :)

I cannot think of anything helpful. f(A) will be a subgroup of Q? I feel like we should have | Q / f(A) | = n but I don't know how to show this.

I'm taking a first course in algebra, and in my textbook, there is the following problem: a) Show that, for every natural # n, there is a subgroup A of Q+ such that |Q+/H| = n. b) Suppose that B is a proper subgroup of Q. Show that |Q / B| = ∞. c) Conclude that Q+ ≠ Q. I did parts a...

It makes sense that it would be true. Let's see. "If a vector space is spanned by a finite number of vectors, then it contains a finite set of vectors which form a basis." Let V be a vector space and let S be a linearly independent set of n vectors which spans V. While the vectors in S are...

Thank you for your reply. The textbook gives only the following definition: "A nonzero vector space V is called finite-dimensional if it contains a finite set of vectors {v1, v2, ... vn} that forms a basis. If no such set exists, V is called infinite-dimensional. " It makes the proof a...

This is an exercise in a linear algebra textbook that I initially thought was going to be easy, but it took me a while to make the proof convincing. Prove: Any subspace of a finite-dimensional vector space is finite-dimensional. Here's my attempt. I am not sure about some details and I'm...

I'm hoping I can get some help with the following question: Does definite integration (from x = 0 to x = 1) of functions in Pn correspond to some linear transformation from Rn+1 to R? OK, well my original answer was yes, but the textbook says "no, except for P0" which I do not understand...

In your solution, you have not assigned a parameter to x1. Your solution is incomplete, basically. You just need to say x1 is a free variable and state x1 = s. In other words, your solution is (x1, x2, x3, x4, x5) = (?, -2-r, 3-r, r, -5) You're asked to state the value of each unknown...

I mean that I know that the solution is x = -1 because I just happened to notice that it was the solution, not because I solved for x = -1. Say I'm left with: e^(x^2-1) = -x I could easily have no idea what the solution is. How do I work the equation to show x = -1?

Homework Statement Hello - I have been messing around with this problem for a while, please help. I actually know the solution, but cannot reach it on paper: Find where the slope of the tangent to the curve e^(-x^2) is equal to 2/e The Attempt at a Solution d/dx e^(-x^2) = e^(-x^2) *...

Thanks all for input. Got my exam results yesterday - scored 100%.

I found n-1 monks dying before repast n. Since breakfast on the eleventh day is the 31st repast, 30 monks will miss breakfast and be found dead in their beds. They all die simultaneously.