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Math Help - Find determinant given a nullspace

  1. #1
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    Find determinant given a nullspace

    The teacher wrote the book, and it is of absolutely no use.

    We're given:

    null(C) =

    1
    2
    3
    4

    and must find the determinant of said matrix C. Any ideas how to approach this? I've spent the past hour going through the book, watching the MIT lectures online, and just generally searching google.
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  2. #2
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    Quote Originally Posted by arcketer View Post
    The teacher wrote the book, and it is of absolutely no use.

    We're given:

    null(C) =

    1
    2
    3
    4

    and must find the determinant of said matrix C. Any ideas how to approach this? I've spent the past hour going through the book, watching the MIT lectures online, and just generally searching google.

    Perhaps it's only me but I just see null(C) = and then a colum with the numbers 1,2,3,4...what is this? What is C: a square matrix with how many rows/columns??

    Tonio
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  3. #3
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    If the null space of any matrix contains any non-zero vectors at all, then it is not invertible and so its determinant is ____.
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  4. #4
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    Quote Originally Posted by tonio View Post
    Perhaps it's only me but I just see null(C) = and then a colum with the numbers 1,2,3,4...what is this? What is C: a square matrix with how many rows/columns??

    Tonio
    It is supposed to represent a single vector, sorry for the formatting confusion.

    The problem simply explains that null(C) is equal to this single 4-vector. As far as I can tell, the zero vector is not given in this null space.
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  5. #5
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    Quote Originally Posted by arcketer View Post
    It is supposed to represent a single vector, sorry for the formatting confusion.

    The problem simply explains that null(C) is equal to this single 4-vector. As far as I can tell, the zero vector is not given in this null space.


    That can't be as any subspace must contain the zero vector. Perhaps it was that the vector (1,2,3,4) is in the null space of the matrix? If so Hallsofivy already gave you an elephant-sized hint.

    Tonio
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