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Math Help - Dimension of columnspace and nullspace

  1. #1
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    Gold Coast, Queensland, Australia
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    Dimension of columnspace and nullspace

    Hi

     A \in \mathbb{C}^{1x3} and  A \neq 0

    What is the dimension of the range and the nullspace?

    I think the columnspace has a dimension of 1 and the nullspace has a dimension of 3, but I'm not exactly sure.
    Can someone confirm this for me please?

    Thanks.
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  2. #2
    Member
    Joined
    Mar 2009
    From
    Gold Coast, Queensland, Australia
    Posts
    105

    Also...

    When we talk about a vector  x \in \mathbb{C}^3
    Are we saying it has a dimension of 3?
    I always thought that but I read something once that confused me and that's why I'm here asking this relatively simple question.
    for the example above the way I would have thought it would have been is this:
     b = Ax and b is in columnspace. and b has the same rows as the matrix so the columnspace in the example above has a dimension of 1.

    the nullspace is all the x's in b = Ax that make it = 0, and the x's have the same number of elements as there are columns in A, so the nullspace is dimension 3.

    Is my thinking right? This is the way I used to think, but somewhere alone the way I read something and now I"m not sure. Can someone please confirm?

    Thanks.
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