C let a be an n n matrix if a j 0 for some integer j

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c) Let A be an n × n matrix. If A j = 0 for some integer j (perhaps j > n ), show that A n = 0. 2-B Let V be a linear space and L : V V a linear map. a) Show that im L 2 im L , that is, if vector b is in the image of L 2 , then vector b is also in the image of L . b) Give and example of a 2 × 2 matrix L where im L negationslash⊂ im L 2 . [Last revised: February 7, 2013] 7
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