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5. Let U = {(u₁, U2, U3) E R³|u₁ + u2 - u3 = 0} and V = {(V1, V2, V3) E R³v₁ - 3v2 +5v3 = 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 R³|u₁ + u2 - u3 = 0} and V = {(V1, V2, V3) E R³v₁ - 3v2 +5v3 = 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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. Let U = {(u₁, U2, U3) € R³ | U₁ + U2 − u3 = 0} and V = {(V₁, V2, V3) € R³ | v₁ - 3v2 +5v3 = 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.
Transcribed Image Text:5. Let U = {(u₁, U2, U3) € R³ | U₁ + U2 − u3 = 0} and V = {(V₁, V2, V3) € R³ | v₁ - 3v2 +5v3 = 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.
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