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 March 30th, 2015, 08:20 PM #1 Member   Joined: Jan 2015 From: Colorado Posts: 32 Thanks: 0 For A to have 0 as an eigenvalue, k must be Let A= matrix [-7 -8] [-4 k] For A to have 0 as an eigenvalue, k must be? When I did this I thought you would just row reduce and figure out what k would be, but I was wrong. If you could help me, that would be greatly appreciated! Thanks  March 30th, 2015, 09:01 PM   #2
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 Originally Posted by mophiejoe Let A= matrix [-7 -8] [-4 k] For A to have 0 as an eigenvalue, k must be?
For $0$ to be an eigen-value the characteristic equation must have $0$ as a root. Here the characteristic equation is $(-7-\lambda)(k-\lambda)-32=0$. Which is equivalent to the constant term being zero, so $-7k-32=0$ ... April 20th, 2015, 09:09 AM   #3
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Quote:
 Originally Posted by mophiejoe Let A= matrix [-7 -8] [-4 k] For A to have 0 as an eigenvalue, k must be? When I did this I thought you would just row reduce and figure out what k would be, but I was wrong. If you could help me, that would be greatly appreciated! Thanks Row reduce to do what? Row reduction does NOT preserve eigenvalues- you cannot use row-reduction to learn anything about eigenvalues. But what is true is that a matrix will have 0 as an eigenvalue if and only if its determinant is 0. Tags eigenvalue, eigenvalues 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 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 Ackoo Linear Algebra 1 May 7th, 2008 07:19 AM lakayii Algebra 1 December 31st, 1969 04:00 PM

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