My Math Forum First uni essay - help needed

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 November 23rd, 2012, 12:30 PM #1 Senior Member   Joined: Jul 2012 Posts: 225 Thanks: 0 First uni essay - help needed Hi, I have a few questions that i need help with. Try and see if you can help please... I'm not from an english speaking country so please bare with me. 1) H1 and H2 are planes in 3d vector space and they aren't parallel. Prove that a third plane H3, contains the intersection line between H1 and H2 if and only if, H3 is a linear summary of H1 and H2 (not sure how to translate it, but you can infer from the connection...pretty sure it's not called linear summary in english) 2) Group E has n subsets contained in it. E is then multiplied by itself, p times. E*E*E....*E - p times. E^p so to speak. How many subsets does the new group E have? 3) Calculate the LU decomposition of the following matrix, or if need, the matrix we get from changing lines 1 2 3 -1 -2 1 2 -3 5 I've never heard or seen the words LU decomposition, no idea what to do here. 4) We are given 2 matrixes, A, and B, both are of the size n*n and that the trace of A (sum of the diagonal line of A) tr(A) is not -1. the goal of this question is to find the matrix M so that: M+tr(M)*A=B a) prove that tr(M)= tr(b)/[1+tr(A)] b) show that M = B - [tr(b)/(a+tr(A))]*A I have more questions but this is enough for now...I'd really appreciate any help I can get, and please explain your answers. I want to understand.

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