2.For this problem, you should only use the definition of a basis, no tricks involving the dimension of avector space.Consider the following set of vectorsS =1123-{E)-(e)}(a) Show that S is not a basis for R³ by showing that it fails one of the defining properties of bases.(b) Construct a basis for R³ using S and the methods covered in class. You must also show that yoursupposed basis satisfies the defining properties of bases.

Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Answered: 2. For this problem, you should only…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.3: Spanning Sets And Linear Independence

Problem 22EQ

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) Consider the vectors -- (-) --- () --- () a = b= = Do these vectors form a basis of R³? If yes, prove that they do, if no explain why.
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The answers must be typed
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n-{() ()}} - {}) 0 )} 12 2 3 B = 3 23 B2 1 3 21 2 2 {)0 ( B3 = B4 4 1 3 -2 a-{() 0} --{) 00} 3 2 B5 B6 = 1 1 2
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