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Math Help - Spanning Set of Null Space

  1. #1
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    Spanning Set of Null Space

    My teacher was out and so I didn't learn this, and yet I have a quiz on the material . . . please help!

    Determine a spanning set for the null space of the given matrix:
    1 2 3 5
    1 3 4 2
    2 4 6 -1

    I would prefer directions or an explanation to an answer - I need to know how to do problems of this type, not this specific problem. Thanks!
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  2. #2
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    Quote Originally Posted by dan213 View Post
    My teacher was out and so I didn't learn this, and yet I have a quiz on the material . . . please help!

    Determine a spanning set for the null space of the given matrix:
    1 2 3 5
    1 3 4 2
    2 4 6 -1

    I would prefer directions or an explanation to an answer - I need to know how to do problems of this type, not this specific problem. Thanks!

    Call your matrix A ,then:

    1) Solve the homogeneous linear system Ax=0 . This is the same as finding the null space of A:

    2) As we know, the above solution is a linear subspace (in this case, of \mathbb{F}^4\,,\,\mathbb{F}= some field) , so now you can choose some spanning set, or even some basis, for it.

    Tonio
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