So if there exists a P such that is diagonal, then A is diagonalizable. where are eigenvectors of A. So, A is diagonalizable if it has 3 distinct eigenvalues.
A is orthogonally diagonalizable if there exists an orthonormal set of 3 eigenvectirs if A. Also, it is orthogonally diagonalizable if there exists P such that is diagonal.
So for (a), I need to show if there is a matrix P that diagonalizes A. First finding the eigenvalues of A:
And I'm stuck here, because I don't know the values of r,p,q. Can anyone help?