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Basis for nullspace of T

  1. Oct 29, 2012 #1
    The problem is attached.

    I am instructed to find a basis for the nullspace of T.


    A basis for a 2x2 matrix is
    1 0
    0 0

    0 1
    0 0

    0 0
    1 0

    0 0
    0 1


    Applying the transformation to each of these gives
    0 0
    0 0

    0 2
    0 0

    0 0
    -2 0

    0 0
    0 0
    respectively.

    Now this is where I get stuck. How do I find a basis after knowing these 4 matrices?

    It look like it's a linear combo of 2 matrices:
    0 1
    0 0
    and
    0 0
    1 0

    but the answer in the book is
    1 0
    0 0

    0 0
    0 1

    I don't undertand.
     

    Attached Files:

    Last edited: Oct 29, 2012
  2. jcsd
  3. Oct 29, 2012 #2

    Mark44

    Staff: Mentor

    Which matrices get sent to (transformed to) the zero matrix? That's the basis for Null(T).
     
  4. Oct 29, 2012 #3
    Gotcha, I keep it getting it cnofused with range (T), nullspace(T) is solved by setting the right hand side of the transformation equal to 0 right?


    So for this case,
    0 1
    0 0
    and
    0 0
    1 0

    would be a basis for the range of T?
     
  5. Oct 29, 2012 #4

    Mark44

    Staff: Mentor

    I think so, but I didn't check your work.
     
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