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1. Eigenval/vect question, double check my answers, dont make sense

eigenval/vect question, double check my answers, dont make sense............. Homework Statement find eigenvalues and eigenvectors of matrix A = 102 012 223 Homework Equations A -λI etc blah The Attempt at a Solution I'm getting λ = 1, -1, 5. For λ = 1, v = (-1,1,0)t (t...
2. Quadric surface question, given 3x3 matrix A and (x^T)Ax=6

this is my working out: http://i.imgur.com/1hsQS.jpg i sort of figured out how to do this a few mins ago lol. it doesnt seem too hard. it's sort of like... multiplying the first number in the matrix A by it's position in the matrix (x1 * x1) which is basically the coordinates of the value...
3. PDE questions

i basically dont know how to do pde's, so i'm learning it from scratch today for my test which is tomorrow (which is in 24hrs from now, for those who dont live in australia), and notes/the internet arent nearly as good as explaining things as people are. so how would i go by starting these...
4. Fourier series of a piecewise function

i'm going through this question. firstly how would the graph look like? at first i thought it would be http://i.imgur.com/XfVCK.png the top graph drawn, but then i thought maybe it's the bottom one. if it was the bottom one then it'd be easier for me to do the question, since it'd be an odd...
5. Laplace transform proof of L{f'(t)}

i can do the majority of laplace questions that will be asked, but i dont understand how to derive the formulae, and this is a past paper question :/ could someone please walk me through this question, or give me some tips?
6. Fourier series question, either i'm wrong or the answers are wrong

Homework Statement Homework Equations The Attempt at a Solution i'm pretty much learning fourier series from scratch today after only looking at it in lectures (and my exam is tomorrow lol @ me) and i'm sort of stuck. The solutions have something different to what i have, i think it might...
7. Laplace heaviside step function question

Homework Statement (quick sketch of part i. yes i know the graph should specifically end at t=4 lol) Homework Equations u(t-a) = 0 for t>a = 1/2 for t=a = 1 for t>a The Attempt at a Solution i'm having trouble solving part (ii). i remember a friend of mine saying something like "start with...
8. Find 2 eigenvectors given an eigenvalue, and find remaining eigenvalue

Could someone please walk me through answering this question: it looks easy but i forgot how to do it -__- i did A - lamda I = 0, substituted lamda = 5, then my matrix became 0 4 4 0 -2 -2 0 -2 -2 so i put in the form of A|b where b was a zero vector and i row reduced, getting 0 1 1 | 0...