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Math Help - basis and dimension

  1. #1
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    basis and dimension

    Bit stuck step by step much appreciated

    decide if each is a basis for r^3

    (1) , (3)
    (2) , (2)
    (3) , (1)

    and

    (0), (1), (0)
    (2), (1), (0)
    (-1), (1), (0)

    help much appreciated
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  2. #2
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    Quote Originally Posted by adam_leeds View Post
    Bit stuck step by step much appreciated

    decide if each is a basis for r^3

    (1) , (3)
    (2) , (2)
    (3) , (1)

    and

    (0), (1), (0)
    (2), (1), (0)
    (-1), (1), (0)

    help much appreciated
    The first one cannot be a basis for it has 2 elements. A basis for \mathbb{R}^3 will need 3 elements.

    And the second one cannot be a basis for it contains the zero vector.
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