Suppose that V is a that has subspaces of U and W. Furthermore, suppose that {u¹, u2} is a basis for U, that {1, 2} is a basis for W and that the only vector that U and W have in common is the zero vector 0. Show that {u¹, u², w¹, w²}. After you get done, note where you used the fact that the only vector common to both U and W is 0. (Without this condition the vectors {u¹, u², w², w2} don't need to be linearly independent, so if you didn't use this condition you definitely made a mistake somewhere.)

Suppose that V is a that has subspaces of U and W. Furthermore, suppose that {u¹, u2} is a basis for U, that {1, 2} is a basis for W and that the only vector that U and W have in common is the zero vector 0. Show that {u¹, u², w¹, w²}. After you get done, note where you used the fact that the only vector common to both U and W is 0. (Without this condition the vectors {u¹, u², w², w2} don't need to be linearly independent, so if you didn't use this condition you definitely made a mistake somewhere.)

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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