Results 1 to 2 of 2

Math Help - Finding a value in a matrix with distinct eigenvalues

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    14

    Finding a value in a matrix with distinct eigenvalues

    The matrix A=\left(\begin{array}{ccc}-1&1&0\\-6&6&1\\k&0&0\end{array}\right)

    has three distinct real eigenvalues if and only if x<k<y. Find x and y.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by chewitard View Post
    The matrix A=\left(\begin{array}{ccc}-1&1&0\\-6&6&1\\k&0&0\end{array}\right)

    has three distinct real eigenvalues if and only if x<k<y. Find x and y.

    1) Calculate the characteristic polynomial of A ;

    2) A polynomial f(x) has a multiple root \alpha iff f(\alpha)=f'(\alpha)=0 ;

    3) Using the above check what could be be the possible multiple roots of the char. pol. of A and what have to be the values of k that'd allow such a thing to happen.

    Tonio
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distinct eigenvalues of a normal matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 26th 2011, 08:32 AM
  2. Finding the eigenvalues of a 3x3 matrix
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: July 30th 2009, 02:32 PM
  3. Finding the eigenvalues of a 4x4 matrix?
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: November 6th 2008, 05:25 AM
  4. Replies: 1
    Last Post: May 6th 2008, 07:24 AM
  5. Accuracy of finding eigenvalues of defective matrix
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 6th 2007, 02:16 AM

Search Tags


/mathhelpforum @mathhelpforum