Could you help giving me explanation on the problem below ? Thank you. Linear Algebra

Let T be an invertible linear operator on a finite dimensional vector space V with dim(V) = n. Suppose )1, 12, and 3 are the distinct eigenvalues of T. Prove that if dim( Ex, ) = n - 2, then T is diagonalizable.Theorem 5.1. A linear operator T on a finite-dimensional vector space V is diagonalizable if and only if there exists an ordered basis 3 for V consisting of eigenvectors of T. Furthermore, if T is diagonalizable, B = {v1, v2, . . ., Un} is an ordered basis of eigenvectors of T, and D = [T]s, then D is a diagonal matrix and Di is the eigenvalue corresponding to vj for 1