Nilpotent matirx (1 Viewer)

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1. If B is any nilpotent matrix prove that I - B is invertible and find a formula for (I-B)^-1 in terms of powers of B?



2. cant seem to figure out how to get the answer to this one, drawn a mental blank any help would be appreciated
 
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so B^k = 0 for some k

say B^2 = 0,

Notice (I-B)(I + B) = I

Now what if B^3 = 0

then (I-B)*something = I


generalize
 

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