(b) If V = U OW is a direct sum of subspaces U, W C V then any element v E V can be written uniquely as v = u +w with u E U and w E W. Show that t(v) =u defines a linear map t: V → V. (c) Show for the map n constructed in (b) that Im(t) U and Ker(t) = W. %3D

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A: Note:  As you requested only Part C(I) so I answered here only that.

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Q: Determine whether W is a subspace of V

A: Determine whether W is a subspace of V

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