Consider a 2 × 2 matrix A with A² = A. a. If w is in the image of A, what is the relationship between w and Aw? b. What can you say about A if rank(A) = 2? What if rank(A) = 0? c. If rank(A) tion T (x) = Ax is the projection onto im(A) along ker(A). See Exercise 2.2.33. 1, show that the linear transforma-

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