(adsbygoogle = window.adsbygoogle || []).push({}); 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？

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

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