Problem 4 (Sums and direct sums) Let U, W be subspaces of a vector space V. Show that:(a) UV is a subspace of V.(b) U and W are both contained in U + W.(c) UW is the smallest subspace containing U and W, that is, U + W = span(U, W).(d) WWW.

Step 1:Let's solve each part one by one:(a) U+W is a subspace of VWe know that the sum of two…

Answered: Problem 4 (Sums and direct sums) Let U,…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.2: Vector Spaces

Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...

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Problem 4 (Sums and direct sums) Let U, W be subspaces of a vector space V. Show that: (a) UV is a subspace of V. (b) U and W are both contained in U + W. (c) UW is the smallest subspace containing U and W, that is, U + W = span(U, W). (d) WWW.