Recent content by hello95

Hello, I am a math and statistics double major, and basically I have a guaranteed unpaid internship opportunity this summer. I have yet to send out applications to other organizations/REUs. While I am interested in the long term in consulting/finance and industrial modeling, I hope to get...

Ah, I see what you're saying. Thank you for the response, I guess my solution wasn't as elegant as I had thought haha. Even if I was able to show that the equations were nontrivial it would end up being a lot more complex than the official solution.

That's from page 67 of Multivariable mathematics (4th edition) by Williamson and Trotter.

Here we go: "A homogeneous system Ax = 0 has only the zero solution if Ax = 0 has at least as many nontrivial equations as variables."

I apologize if I'm wrong, I haven't done much work with matrix algebra as I have only taken theory-based linear algebra (Axler).

Well each entry will be 1 or 0, and each combination of 1s and 0s in each row will be different, because each square is unique. There will be 4 1's in each row. Wouldn't that imply that you cuold put the matrix into eschelon form, solving for each a(i)?

Here is the problem: Let f be a real-valued function on the plane such that for every square ABCD in the plane, f(A) + f(B) + f(C) +f(D) = 0. Does it follow that f(P) = 0 for all points P in the plane? Below is my solution: Create a 3x3 set of boxes (where each box has equal...

Wikipedia says that there are 92 ways of solving the problem though, so I don't know.

well come to think of it, each queen eliminates two diagonals, so I'm not sure it would ever work

Actually I'm not sure if it does work now that I'm trying to work it out... each queen eliminates a row, column, and diagonal from future options of where to place the next queen. Eventually the eliminated columns and diagonals amount to eliminating a row no matter how you place the first 4 or 5...

^I remember that problem. It's possible if I remember correctly

D wasn't really meant to be a function by the way, just a way of signifying the concept

so are we talking a series of pawns (p(1), p(2), ... , p(8)) such that D(p(i)) - D(p(i + 1)) is different for every i? Because something like a conch shell spiral works if that's the case. More generally I think with any nxn board it should be possible to place n pawns at different distances...

Equate gravitational potential energy with kinetic energy of the gas for a given radius and density, and then find the mass from that.

So I just got out of my linear algebra midterm, and this question is confusing the hell out of me. Basically, it's a subspace of R^4, such that the coordinates satisfy the following qualifications: (a, b - a, b, 2(b - a)) So basically, a and b can range over the xz plane, and y and w sort...