Summer 2002 done - (15 pts)1 Let T R2 R2 be a linear...

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(15 pts)1.LetT:R2-→R2be a linear transformation with the property thatT31=2-4,T11=02.Let~e1, ~e2denote the standard basis forR2.(1) CalculateT(~e1) andT(~e2).(2) What isT(~x) for an arbitrary vector~x=x1x2inR2?(3) Find the matrix representing T with respect to the basis:B={12,21}.Solution:
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(15 pts)2.A=-403(1) Find the characteristic polynomial ofA.(2) Find the eigenvalues ofA.(3) Find a basis for each eigenspace ofA.-101-301
(15 pts)

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