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Geometric description of the nullspace

  1. Nov 8, 2009 #1
    1. The problem statement, all variables and given/known data
    general form of solutions to Ax=b
    Consider matrix A=
    {[ 2 -10 6 ]
    [ 4 -20 12 ]
    [ 1 -5 3 ]}
    Find a basis for the nullspace of A. Give a geometric description of the nullspace of A.


    3. The attempt at a solution
    I found the basis for the nullspace of A to be
    {[-3 5]
    [0 1 ]
    [1 0 ]}
    The thing i dont understand is how to give a geometric description of the nullspace of A. If someone could help to explain how i would start to go about doing this that would be awesome because i'm not quite sure i understand the question.
     
  2. jcsd
  3. Nov 8, 2009 #2
    Are you saying that your null space is spanned by {-3, 0, 1} and {5, 1, 0}? Your notation is a bit confusion to me; but I believe that they are asking you to describe what kind of "Space" this is. What do two vectors span?
     
  4. Nov 8, 2009 #3
    I was trying to say that the vectors {-3,0,1} and {5,1,0} form the basis for the nullspace of A and that i'm not seeing how to give a geometric description of the nullspace of A.
     
  5. Nov 8, 2009 #4

    Mark44

    Staff: Mentor

    How many linearly independent vectors does it take to span a line? A plane? A three-dimensional space?
     
  6. Nov 8, 2009 #5
    one linearly independent vector to span a line, two linearly independent vectors to span a plane, and 3 linearly independent vectors to span a 3-dimensional space, and so forth any n vectors that span an n-dimensional space are going to be linearly independent. So i see i'm going to have 2 linearly independent vectors and therefore the dim(W) is going to be 2 dimensional like i thought. Question: Can the vectors ever be identical say that v1=v2
     
  7. Nov 8, 2009 #6

    Mark44

    Staff: Mentor

    Linearly independent vectors can't be identical or even multiples of one another.
     
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