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Homework Help: A similar question on finding the values for which its digonolized

  1. Mar 2, 2008 #1
    http://img139.imageshack.us/my.php?image=img86081ca6.jpg

    first i am given an all 1 matrix
    and i was asked to find the eigenvalues
    and the eigenvectors of this metrix

    then i was told to find the orthonormal basis of this matrix
    so i took the vectors that i have got
    i made an gram shmidt formula on the two eigenvectors which came out of
    the 0 eigenvalue and divided each vector of the resolt by its NORMA

    after that i took the remainding third eigenvector and i divided him by his norma
    is it ok??
    (this is how i was told to solve this kind of question
    but if a have only a simple matrix and i want to turn it into orthonormal
    and i dont have such a relations between the columns as here(regarding the eigenvalues)
    what should i do then??(this is only a subquestion not the main one)

    then i was given an all "z" matrix
    and i was told to proove that for each value of Z which belongs to the complex numbers "C" then its diagonizable
    i dont know how to proove that

    so if i put in z=0 then for this option i have only 2 vectors as i showed in the start
    instead of the desiarble 3

    so the answer that i think is z differs 0

    i dont know how to proove what they want
     
    Last edited: Mar 2, 2008
  2. jcsd
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