Let U and W be the subspace of V, with V being the vector space on R body. UnW = {v : v € U ve v e W} be identified with. Prove the statements below. a) Unw, It is the subspace of V. b) Unw= {0}ls. f and only if 0= u € U and 0 # w € W About to be {u, w} le is linearly independent.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 43EQ
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Let U and W be the subspace of V, with
V being the vector space on R body.
UnW = {v :v E U ve v € W} be identified with.
Prove the statements below.
a) UnW, It is the subspace of V.
b) UnW = {0} Is. if and only if 0 u E Uand 0 # w E W
About to be {u, w} It is linearly independent.
%3D
Transcribed Image Text:Let U and W be the subspace of V, with V being the vector space on R body. UnW = {v :v E U ve v € W} be identified with. Prove the statements below. a) UnW, It is the subspace of V. b) UnW = {0} Is. if and only if 0 u E Uand 0 # w E W About to be {u, w} It is linearly independent. %3D
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