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6. a. Let U and V be subspaces of R". Define the intersection of U and V to be UnV = {x € R" : x e U and x e V}. Show that U N V is a subspace of R". Give two examples. b. Is U U V = {x e R" : x e U or x e V} always a subspace of R"? Give a proof or counterexample.

6. a. Let U and V be subspaces of R". Define the intersection of U and V to be UnV = {x € R" : x e U and x e V}. Show that U N V is a subspace of R". Give two examples. b. Is U U V = {x e R" : x e U or x e V} always a subspace of R"? Give a proof or counterexample.

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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linear algebra 3.1 Q6 

6. a. Let U and V be subspaces of R". Define the intersection of U and V to be UNV : {x e R" : x e U and x e V}. Show that U N V is a subspace of R". Give two examples. b. Is U UV = {x € R" : x e U or x e V} always a subspace of R"? Give a proof or counterexample.
Transcribed Image Text:6. a. Let U and V be subspaces of R". Define the intersection of U and V to be UNV : {x e R" : x e U and x e V}. Show that U N V is a subspace of R". Give two examples. b. Is U UV = {x € R" : x e U or x e V} always a subspace of R"? Give a proof or counterexample.
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Step 1

Subspace: Let V be a vector space over the field F and S be a non empty subset of V. Then we say S is a subspace of V of for every 

s1,s2∈S and α∈F,

                                        s1+αs2∈S

 

 

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