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Advanced Linear Algebra : Nilpotent, Vectors, Basis and Linear Independence

Let T: IR^3 IR^3 , T(x,y,z) = (o,x,2y)

- Show that T is nilpotent of index 3 (that is, T^3 = 0 and T^2 different from 0 )

- Find a vector v E IR^3 s.t T^2(v) different from 0 and show that

B = { v, T(v), T^2(v) } is linearly independent (so basis)

- Find A = [ T ] and B = [ T ]
B standard basis

- Find the eigenvalues of T

Please see the attached file for the fully formatted problems.

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Solution Summary

Nilpotent, Vectors, Basis and Linear Independence are investigated. The solution is detailed and well presented.

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