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Homework Help: Matrix and kernel help

  1. Feb 25, 2007 #1
    1. The problem statement, all variables and given/known data
    Express the plane V in 3 with equation 3x1+4x2+5x3=0 as the kernel of a matrix A and as the image of a matrix B.
    {Note: the 1,2, and 3 after the x are subscript}
    2. Relevant Equations

    3. The attempt at a solution
    Would the relevant matrix just be a [3 4 5] with an image of 3?
    Last edited: Feb 25, 2007
  2. jcsd
  3. Feb 25, 2007 #2
    Plane V in 3 ???? Do you mean in R^3?

    You have a lot of room to play with here, since there is not just one single example. Hints:
    For the first part, the dimension of the null space is that of a plane (in R^3) and is of dim 2. The dimension of the row space would be 3-dim null space=1.

    For the second part, I would try to find two vectors that span the given plane (remember 3rd semester calc with analytic geometry? Remember how to find the normal to a plane and how to get two linearly independent vectors perpendicular to that normal?) . That would give you the col. space of the matrix. As you need three columns, you can take one of the col.'s to be a linear combination of two others you have derived.
    Good Luck
  4. Feb 26, 2007 #3


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    Science Advisor

    Do you understand that you are asked for two matrices, A and B?
    You might want to review the definitions of "kernel of a matrix" and "image of a matrix".
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