Exercise 3.6. Interpret geometrically what it means for two vectors u and v to be linearly independent in R². What about R³? Prove that: (i) Any two vectors u,ve R³ are linearly independent if and only if they are not parallel to each other. (ii) If u,v are linearly independent then Span (u, v) is the plane passing through the origin and determined by u and v. (iii) Any three vectors u,v, w € R³ are linearly independent if and only if they are not coplanar. (iv) If u,v,w are linearly independent then Span (u,v,w) is all of R³.

Exercise 3.6. Interpret geometrically what it means for two vectors u and v to be linearly independent in R². What about R³? Prove that: (i) Any two vectors u,ve R³ are linearly independent if and only if they are not parallel to each other. (ii) If u,v are linearly independent then Span (u, v) is the plane passing through the origin and determined by u and v. (iii) Any three vectors u,v, w € R³ are linearly independent if and only if they are not coplanar. (iv) If u,v,w are linearly independent then Span (u,v,w) is all of R³.

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 38EQ

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