So it seems to be that you have to prove that the matrix A is not diagonalizable...well, you know that a matrix is diagonalizable iff there's a basis (of the vector space on which it acts) formed by eigenvectors of the matrix: have you already evaluated all the eigenvectors of the matrix corresponding to its eigenvalues?
i think so i got -4x+5y=0 as one and 4x-5y=0 as the other usinng the eigenvalue 7 which i think means itany non zero vector in which 4x=5y is an eigenvecotr
the second one corresponding to the eigenvalue 2 is 5x+5y=0 andn 4x+4y=0 therefroe any non zero vector in which 4x=5y is an eigenvecotr corresponding to the eigenvalue -2
i think that is right but i thought for example -4x+5y=0 and 4x-5y=0 should be the same ???