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7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW.

Advanced Engineering Mathematics
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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7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW. V = U +W and have just proved that Un W = {0}; hence, V = UO W. %3D 8)
Transcribed Image Text:7) Assume dim V = n, dim U = k, dim W = n - k, and U + W = V. Prove that Un W = {0} and V = U OW. V = U +W and have just proved that Un W = {0}; hence, V = UO W. %3D 8)
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