Let V be a vector space over a field F with zero vector 0 and let S, T be subspaces of V.Then which of the following statements are false?0 is in S.For every EV,+Sis a subspace of VS+S+SUT is a subspace of WSnT is a subspace of V.

1st Statement is True : S being a subspace of V, it must contain the zero element. So, 0 belongs to…

Answered: Let V be a vector space over a field F…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let V be a vector space over a field F with zero vector 0 and let S, T be subspaces of V. Then which of the following statements are false? 0 is in S. For every eV,+S is a subspace of V. S+S+S. SUT is a subspace of W SnT is a subspace of V.