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Suppose V is finite-dimensional and T 2 L.V /. Prove that the followingare

Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition | ISBN: 9783319110790 | Authors: Sheldon Axler ISBN: 9783319110790 432

Solution for problem 3 Chapter 5.C

Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition

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Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition | ISBN: 9783319110790 | Authors: Sheldon Axler

Linear Algebra Done Right (Undergraduate Texts in Mathematics) | 3rd Edition

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Problem 3

Suppose V is finite-dimensional and T 2 L.V /. Prove that the followingare equivalent:(a) V D null T range T.(b) V D null T C range T.(c) null T \ range T D f0g.

Step-by-Step Solution:
Step 1 of 3

7/26/2017 OneNote Online 2.5 Monday, September 8, 28:51 PM https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!2562&cid=36773184373a8f0b&app=OneNote&authkey=Avz_e_hLmB4xJLw 1/5 7/26/2017 OneNote Online https://onedrive.live.com/view.aspxref=button&Bsrc=SMIT&resid=36773184373A8F0B!2562&cid=36773184373a8f0b&app=OneNote&authkey=Avz_e_hLmB4xJLw 2/5

Step 2 of 3

Chapter 5.C, Problem 3 is Solved
Step 3 of 3

Textbook: Linear Algebra Done Right (Undergraduate Texts in Mathematics)
Edition: 3
Author: Sheldon Axler
ISBN: 9783319110790

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Suppose V is finite-dimensional and T 2 L.V /. Prove that the followingare