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anonymous
 5 years ago
prove that an nxn nilpotent matrix always has det=0
anonymous
 5 years ago
prove that an nxn nilpotent matrix always has det=0

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know that at some point A^n=0, and therefore the determinant is zero, but I must also have to prove that the matrices before it becomes zero have a determinant of zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0and det(0)=0=A^n....and A^n is connected to A somehow

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0use the fact det[A^n] = [det A]^n

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok, so that would conclude the proof, because only 0^n can give zero

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0just like x^n = 0, the only solution is x must be 0
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