Let T: V → V be a linear operator whose characteristic polynomial is pT(x)=x2(x−1)3(x+2)2. Judge each item below as true or false. (A) Let A be the matrix of T with respect to some basis of V. If A(A−I)(A+2I) = 0, then T is diagonalizable. (B) The roots of the minimal polynomial of T are 1 and −2. (C) If the minimal polynomial of T is x(x−1)(x+2) then there is a basis of V formed by eigenvectors.

Let T: V → V be a linear operator whose characteristic polynomial is pT(x)=x2(x−1)3(x+2)2. Judge each item below as true or false. (A) Let A be the matrix of T with respect to some basis of V. If A(A−I)(A+2I) = 0, then T is diagonalizable. (B) The roots of the minimal polynomial of T are 1 and −2. (C) If the minimal polynomial of T is x(x−1)(x+2) then there is a basis of V formed by eigenvectors.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.4: Similarity And Diagonalization

Problem 51EQ

See similar textbooks