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 February 4th, 2015, 12:19 PM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Eigenvalue of matrix I have a matrix M, and I am trying to find the eigenvalues + eigenvector for this matrix $\displaystyle \left( \begin{array}{ccc} 1-x & x \\ y & 1-y \end{array} \right)$ 0 = det ( M - λI) 0 = λ^2 + λ(y + x -2) + 1 -x Not sure how to find the roots from here. The only other information I know is that x an y are between 0 and 1. But im not sure how that helps me. Any help if much appreciated. Last edited by calypso; February 4th, 2015 at 12:23 PM. February 4th, 2015, 12:56 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra Use the quadratic formula$$\lambda = \tfrac12 \left(2-x-y \pm \sqrt{ (y+x-2)^2 + 4(x-1) }\right)$$ February 4th, 2015, 01:01 PM #3 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Thanks, yes I did try and use the quadratic formula. I got a similar answer to what you have posted. I suppose I expected the answer to produce 2 distinct roots. Maybe it doesnt and the furthest you go is to write what you have posted. February 4th, 2015, 02:16 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,681 Thanks: 2659 Math Focus: Mainly analysis and algebra That is two roots. One where the $\pm$ is a plus, the other where it's a minus. Tags eigenvalue, matrix Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post subhajit028 Linear Algebra 3 September 16th, 2013 12:00 PM lakayii Linear Algebra 2 September 24th, 2012 07:48 AM wannabe1 Linear Algebra 2 April 17th, 2010 02:33 PM tinynerdi Linear Algebra 3 April 5th, 2010 12:56 AM lakayii Algebra 1 December 31st, 1969 04:00 PM

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