Results 1 to 2 of 2

Math Help - Very simple true or false

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    21

    Very simple true or false

    If λ is an eigenvalue of a matrix A, then there exist infinitely many vectors x such
    that Ax = λx. True or False?
    I'm guessing that it is true since we will have a general solution where any number can be placed in the variable.
    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7

    Re: Very simple true or false

    Quote Originally Posted by farmeruser1 View Post
    If λ is an eigenvalue of a matrix A, then there exist infinitely many vectors x such
    that Ax = λx. True or False?
    I'm guessing that it is true since we will have a general solution where any number can be placed in the variable.
    Thanks
    The definition of eigenvalue tells you that there must be at least one eogenvector x. But if x is an eigenvector then so is any nonzero scalar multiple of x. So the answer is going to depend on how many elements there are in the field of scalars.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: October 5th 2011, 01:45 PM
  2. Replies: 1
    Last Post: October 4th 2011, 03:19 AM
  3. how come false AND false is true?
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: September 24th 2010, 08:41 AM
  4. True or False. Prove if true show counter example if false.
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: March 2nd 2010, 11:54 AM
  5. Some Simple True/False
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: February 27th 2010, 12:28 PM

Search Tags


/mathhelpforum @mathhelpforum