Let V be a vector space and W be a subspace of V. For any vector x E 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 E V We Let X W X W W W Fix X Y V Prove 1 (29.95 KiB) Viewed 44 times

Let V be a vector space and W be a subspace of V. For any vector x E 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 € W. 2. x + W = y + W if and only if x - y E W.