a similar question on finding the values for which its digonolized..

transgalactic

http://img139.imageshack.us/my.php?i...mg86081ca6.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