3. (15%) Let T be a linear transformation and \( \lambda_1, \lambda_2, \dots, \lambda_n \) be      distinct      eigenvalues of T . If \( \vec{v}_1, \vec{v}_2, \dots, \vec{v}_n \),  are eigenvectors of T such that λi corresponds to  \( \vec{v}_i \) (1 ≤ i ≤ n ), Prove that \( \vec{v}_1, \vec{v}_2, \cdots, \vec{v}_n \) are linear independent.