Answered: Suppose U1; U2; :::; Um are…

Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V . Prove that U1 + U2 + ::: + Um is Önite-dimensional and dim(U1 + U2 + ::: + Um) dim U1 + dim U2 + ::: + dim Um

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 18CM

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Question

Suppose U1; U2; :::; Um are Önite-dimensional subspaces of V .
Prove that
U1 + U2 + ::: + Um is Önite-dimensional
and
dim(U1 + U2 + ::: + Um) dim U1 + dim U2 + ::: + dim Um

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