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Below is a proof of Theorem 4.1.1 (b): For the zero vector ?0 in any vector...

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Advance Math

  1. Below is a proof of Theorem 4.1.1 (b): For the zero vector ?0 inany vector space V and k ? R, k?0 = ?0.

    Justify for each of the eight steps why it is true.

    1. k?0+k?0=k(?0+?0)

    2. = k ?0

    3. k?0 is in V

    4. and therefore ?(k?0) is in V .

    5. It follows that (k?0 + k?0) + (?k?0) = (k?0) + (?k?0)

    6. and thus k?0 + (k?0 + (?k?0)) = (k?0) + (?k?0).

    7. We conclude that k?0 + ?0 = ?0

    8. and so k?0 = ?0, as desired.

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