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1. Let SC R be the subset S = {(0, y,0)" | y € R}. Prove that if ī, w e S and a E R, then i+ w ES and au E S. (This is what it means to prove that S is closed under addition and scalar multiplication.) 2. Let V be a vector space over R. Prove that if a E R and a 0, then að = 0.

1. Let SC R be the subset S = {(0, y,0)" | y € R}. Prove that if ī, w e S and a E R, then i+ w ES and au E S. (This is what it means to prove that S is closed under addition and scalar multiplication.) 2. Let V be a vector space over R. Prove that if a E R and a 0, then að = 0.

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1. Let S C R³ be the subset S = {(0, y,0)" | y ER}. Prove that if 7, w E S and a E R, then & + w E S and au E S. (This is what it means to prove that S is closed under addition and scalar multiplication.) 2. Let V be a vector space over R. Prove that if a E R and a + 0, then a0 = 0.
Transcribed Image Text:1. Let S C R³ be the subset S = {(0, y,0)" | y ER}. Prove that if 7, w E S and a E R, then & + w E S and au E S. (This is what it means to prove that S is closed under addition and scalar multiplication.) 2. Let V be a vector space over R. Prove that if a E R and a + 0, then a0 = 0.
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