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Math Help - Linear algibra - Vector space problem

  1. #1
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    Linear algibra - Vector space problem

    This is my question please give me a help to find answer

    Let V be the set of ordered pairs (a, b) of real numbers. Show that V is not a vector space over \mathbb{R}
    with vector addition and scalar multiplication defines by:
    01. (a, b) + (c, d) = (a + c, b + d) and k(a, b) = (a, kb)
    02. (a, b) + (c, d) = (a + c , b + d) and k (a, b) = (o , kb)
    03. (a, b) + (c, d) = (ac, bd) and k(a, b) = (ka, kb)
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  2. #2
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    Where are you having diffficulties? Do you know what you should be looking at?
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  3. #3
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    Thank you very much for Ur reply,
    Actually I couldn't understand this question well. Here the 03 rules are defined and then we need to prove the V is not a vector space over  \mathbb{R}
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  4. #4
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    In other word, for each of the three kinds of operations defined, determine whether or not they obey the requirements for a vector space:
    Addition is associative and commutative, there exist an additive identity and every element has an additive inverse, scalar multiplication is associative and commutative, and scalar multiplication distributes over addition.
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