13. Let U, W be vector subspaces of a vector space V. If dim(U) 3, dim(W) 4, dim(V) = 7 and UnW = {0} prove that U + W = V.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
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Chapter4: Vector Spaces
Section4.3: Subspaces Of Vector Spaces
Problem 13E: Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by...
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Can you solve both questions pls
= 3, dim(W)
13. Let U, W be vector subspaces of a vector space V. If dim(U)
4, dim(V) = 7 and UnW = {0} prove that U + W = V.
14. Show that cancellation low holds in any vector space; that a 0 vector is unique
in any vector space; intersection of two vector subspaces is a vector subspace as
well; that any vector can be seen in an unique way as a linear combination of the
vectors in the basis.
Transcribed Image Text:= 3, dim(W) 13. Let U, W be vector subspaces of a vector space V. If dim(U) 4, dim(V) = 7 and UnW = {0} prove that U + W = V. 14. Show that cancellation low holds in any vector space; that a 0 vector is unique in any vector space; intersection of two vector subspaces is a vector subspace as well; that any vector can be seen in an unique way as a linear combination of the vectors in the basis.
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