Results 1 to 4 of 4

Math Help - eigenvalues and vectors

  1. #1
    Newbie
    Joined
    Nov 2006
    Posts
    10

    eigenvalues and vectors

    hi.
    i need to find the eigenvalues and eigenvectors of the following matrix.

    ( 7 -6 )
    ( -6 -2 )

    i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.
    thanks for the help
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mesterpa View Post
    hi.
    i need to find the eigenvalues and eigenvectors of the following matrix.

    ( 7 -6 )
    ( -6 -2 )

    i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.
    thanks for the help
    sorry, but those are wrong:

    recall that to find the eigenvalues, we find det((lambda)In - A)

    where In is the identity matrix and A is the matrix you're working on. i will use L for lambda, since i cant bother typing lambda all the time.

    For eigenvalues:

    det(L*In - A) = 0

    (L..........0)......-.......(7...........-6)
    (0..........L)..............(-6..........-2)

    = (L - 7.........6)
    ...(6.......... L+2)

    det(L - 7.........6) = 0
    ....(6.......... L+2)
    => (L - 7)(L + 2) - 36 = 0
    => L^2 -5L - 50 = 0
    => (L + 5)(L - 10)=0

    so L1 = -5, L2 = 10 .............these are the eigen values
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by mesterpa View Post
    hi.
    i need to find the eigenvalues and eigenvectors of the following matrix.

    ( 7 -6 )
    ( -6 -2 )

    i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.
    thanks for the help
    I think you are wrong.
    Attached Thumbnails Attached Thumbnails eigenvalues and vectors-picture13.gif  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mesterpa View Post
    hi.
    i need to find the eigenvalues and eigenvectors of the following matrix.

    ( 7 -6 )
    ( -6 -2 )

    i worked out the eigenvalues to be -2 and 7. can anyone tell me if these are right. not sure how to get eigenvectors.
    thanks for the help
    to get the eigenvectors, you use (L*In - A)x = 0 where x is a vector of with components x1, x2 ....

    so for each eigenvector, you plug in its value into the matrix that we formed, solve for the unknowns and place them in a solutions vector, these vectors will be your eigen vectors
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problem involving eigenvalues/vectors
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 23rd 2011, 05:44 AM
  2. Eigenvalues/vectors
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: August 3rd 2010, 02:55 AM
  3. eigenvalues and vectors related proof
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 19th 2009, 08:42 AM
  4. Eigenvalues and eigen vectors
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: April 27th 2009, 02:17 PM
  5. eigenvalues and eigen vectors!
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: July 11th 2007, 08:25 AM

Search Tags


/mathhelpforum @mathhelpforum