Let V be a vector space and W be a subspace of V. For any vector x € V, we let x + W = {x+w: w€ W}. Fix x, y € V. Prove

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Let V Be A Vector Space And W Be A Subspace Of V For Any Vector X V We Let X W X W W W Fix X Y V Prove 1 (37.25 KiB) Viewed 27 times

Let V be a vector space and W be a subspace of V. For any vector x € V, we let x + W = {x+w: w€ W}. Fix x, y € V. Prove the following: 1. x + W is a subspace of V if and only if x E W. 2. x + W = y + W if and only if x − y ≤ W.