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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 26EQ

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LINEAR ALGEBRA
PLEASE ANSWwER ALL QUESTIONS
Let T:V → V be a linear operator on a finite-dimensional vector space V over C such that T² = T.
.1 Show that R(T) C N(T – I) and R(T – I) C N(T).
2 Show that V- R(T) + R(T – I).
3 Show that V = N(T) ® N(T – I).
%3D
4 Show that T is diagonalisable.
06:43 PM
2022-05-10
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