answer part iv and v show proper working (b) Let T: R³ R³, T(v) = (v. w;)w; +(v,w₂)w, where w; = (1,-1,0) and w₂ = (0,-2,1).(1) Find the kernel of 7.(ii) Find the range of T.(iii) Find the nullity and rank.(iv) Determine whether T is one-to-one and onto. Justify your answer.(v) Is it an isomorphism? Justify your answer.

Answered: Image /qna-images/answer/a0d7898e-b4ed-4e6c-a718-944d2fca2182.jpg

Answered: (b) Let T: R³ →R³, T(v) = (v₂w;)w; +(v,…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.6: Applications And The Perron-frobenius Theorem

Problem 70EQ

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(b) Let T: R³ →R³, T(v) = (v₂w;)w; +(v, w,₂)w, where w, = (1,-1,0) and w₂ = (0,2,1). (1) Find the kernel of T. (ii) Find the range of T. (iii) Find the nullity and rank. (iv) Determine whether T is one-to-one and onto. Justify your answer. (v) Is it an isomorphism? Justify your answer.