Recent content by Niels

thank you!

I'm trying to learn probability on my own and I'm stuck. My multiple-variable-calculus is not so strong so the following problem got me stuck. I have density function f(x,y) = x^2 + xy/3 for 0<x<1; 0<y<2 otherwise 0 And I need to calculate Prob(X > Y). X and Y are random variables...

The graphs are undirected without loops...

I'm having an exam on graph theory next week and I'm having some problem with understanding the meaning of calculating eigenvalues of adjacency matrices for graphs. My notes suck from the lectures and I'm totally lost... Our professor asked "What is the sum of elements in row k of the...

Thanks! I know now that I'm stupied :)

Ok,sorry here's the whole text: Let A be an nxn matrix, and suppose A har n real eigenvalues \lambda_1 ... \lambda_n repeated accordingly to multiplicities, so that det(A - \lambda I) = (\lambda_1 - \lambda)*(\lambda_2 - \lambda)*...*(\lambda_n - \lambda) Explain why det(A) is the product...

How do you prove that det(A) = \lambda_1*\lambda_2*...*\lambda_n, where \lambda_i is the eigenvalues of A? I'm stuck :cry:

Yes, n is integer (input size for algorithm) but I'm interested in both cases. (real/integer)

I already did that with mathematica and got that one solution is x ~ 6.5... I just wanted to know if there was any algebraic solution... I study running times of some algorithms and got this questions: for that values of n is the following inequality true: 8n^2 < 64 n lg(n) Is there no...

How do I solve the following equation? 8n^2 = 64 n lg(n); (0 < n) n = 8lg(n) 10^n = 10^8 n ...? How do I isolate n?