Department of Mathematics, University of Toronto MAT224H1S - Linear Algebra II Winter 2016 Writing Assignment 6 1. Let V be a 5-dimensional vector...

Let V be an n-dimensional vector space, and T : V → V a linear transformation.Show that T is nilpotent of order (index) n if and only if there exists a basis β ={v1, v2, . . . , vn} of V such that the matrix of T relative to β is of the form