- #1
manuel325
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Homework Statement
Let ##L: R^{2} → R^{2}## be a linear map such that ##L ≠ O## but## L^{2} = L \circ L = O.##
Show that there exists a basis {##A##, ##B##} of ##R^{2}## such that:
##L(A) = B## and ##L(B) = O.##
The Attempt at a Solution
Here's the solution my book provides :
Well I have two questions:
1.Why do they say that ##aA+bB=O##?. I mean I don't understand the solution from that point until the end (Why the solutions ##a=0## and ##b=0## are enough to prove the existence of that basis??May someone please explain??
Thanks in advance