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Linear algebra - transformations

  1. Jan 16, 2008 #1
    [SOLVED] Linear algebra - transformations

    1. The problem statement, all variables and given/known data
    Please take a look at:


    Please take a look at #7, question c. To determine if the vector w is in the image (range) of T, I find the matrix B that represents the linear transformation T and find the solution to the system:

    Bx = w,

    because w has to be in the span of B (which I found to be the image of T). If it is consistent, w is in the range of T?

    Thanks in advance,

    sincerely Niles.
    Last edited: Jan 16, 2008
  2. jcsd
  3. Jan 16, 2008 #2


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    It's not clear to me what the "span" of a matrix would be! I think you mean the span of the vectors making the columns of the matrix T. Yes, that span, the "column space" of T is the image of the T and "image" is the "range" here. The crucial point is exactly how you show that w is in the image of T.
  4. Jan 16, 2008 #3
    I have the vectors that span the column space. I put these vectors together in a matrix I call B, and I write a new matrix <B|w>, and solve this. If consistent, w is in the column space.

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