3) Let Vi, V2 C V be subspaces. Let T : V → W be linear. Prove that T(V1 + V½) = T(Vi) + T(V2).

Elementary Linear Algebra (MindTap Course List)
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Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 54CR: Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector...
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Unless otherwise stated, F is a field. V , W, and X are vector spaces over F.

3) Let Vi, V2 C V be subspaces. Let T : V → W be linear. Prove that
T(V1 + V½) = T(Vi) + T(V2).
Transcribed Image Text:3) Let Vi, V2 C V be subspaces. Let T : V → W be linear. Prove that T(V1 + V½) = T(Vi) + T(V2).
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