5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a) Show that U and V are subspaces of R³. (b) Is the set U UV:= {x|x EU or x E V} a subspace of R³? Justify your answer. (c) Is the set UnV:= {x|x EU and x E V} a subspace of R³? Justify your answer.

5. Let U = {(u1, U2, U3) E R3³|u₁ + u2u3 = 0} and V = {(v₁, V2, V3) E R³|v1 - 302 +503 = 0}. (a) Show that U and V are subspaces of R³. (b) Is the set U UV:= {x|x EU or x E V} a subspace of R³? Justify your answer. (c) Is the set UnV:= {x|x EU and x E V} a subspace of R³? Justify your answer.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.1: Vector Spaces And Subspaces

Problem 42EQ

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