6. Let U, VCR" be subspaces, and define U+V = {u+v: u € U₂v € V}. 2 (a) Prove U + V is a subspace of R". (b) If UnV= {0}, prove dim(U+V) = dim U + dim V.
6. Let U, VCR" be subspaces, and define U+V = {u+v: u € U₂v € V}. 2 (a) Prove U + V is a subspace of R". (b) If UnV= {0}, prove dim(U+V) = dim U + dim V.
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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Transcribed Image Text:6.
Let U, VCR" be subspaces, and define
U + V = {u+vu € U₂v € V}.
2
(a) Prove U + V is a subspace of R".
(b) If UnV = {0}, prove dim(U + V) = dim U + dim V.
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