Let T ≤ L(V). Suppose T has the matrix representation with respect to a basis B = {V₁, ..., v6} for V given by [T] B = 2 12 [T]c= 12 (a) Find a basis C for V such that the matrix associated to T is 3 1 3 2 1 2 1 2 3 1 3 (b) What are the characteristic polynomial and minimal polynomial for T? (c) What are the eigenspaces and their dimensions?

Let T ≤ L(V). Suppose T has the matrix representation with respect to a basis B = {V₁, ..., v6} for V given by [T] B = 2 12 [T]c= 12 (a) Find a basis C for V such that the matrix associated to T is 3 1 3 2 1 2 1 2 3 1 3 (b) What are the characteristic polynomial and minimal polynomial for T? (c) What are the eigenspaces and their dimensions?

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.6: Introduction To Linear Transformations

Problem 55EQ

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