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A 2*2 matrix A with A^2= A

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data
    a 2*2 matrix A with A^2= A
    1)if vector w is in the image of A , what is the relationship between vector w and A*w

    2. Relevant equations
    2)what can say about A if rank(A)= 2 , what if rank(A)=0
    3)if rank(A) = 1,show that the linear transformation T(x)=Ax is the projection onto im (A) along ker(A)


    3. The attempt at a solution
    to the 1), does the A^2*w= A w, and w is in the image of A, so the both w and Aw is in image A?
     
  2. jcsd
  3. Sep 20, 2011 #2

    micromass

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    What does it mean that w is in the image of A?? Can you write w=... in a special way??
     
  4. Sep 20, 2011 #3
    so vector w is in im ( A)
     
  5. Sep 20, 2011 #4

    micromass

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    Yes, and what does it mean that w is in im(A)?
     
  6. Sep 20, 2011 #5

    vector w belons to the image of matrix A, and the image of linear transformation Ax is the span of the column vector in A
     
  7. Sep 20, 2011 #6

    micromass

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    Can you prove that there exists an x such that w=Ax??
     
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