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4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such that U = {[y]: x, y = F} and W = {[ ] : x, y = F}. x Then, show that V = UW.

4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such that U = {[y]: x, y = F} and W = {[ ] : x, y = F}. x Then, show that V = UW.

Elementary Linear Algebra (MindTap Course List)
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 5CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...
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4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such that U = {[y]: x, y = F} and W = {[ ] : x, y = F}. x Then, show that V = UW.
Transcribed Image Text:4) Let VM2x2(F) be the set of all matrices of size 2 × 2 and let U and W be two subspaces of V such that U = {[y]: x, y = F} and W = {[ ] : x, y = F}. x Then, show that V = UW.
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