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For the linear operator T on V , find an ordered basis for the T -cyclic...

For the linear operator T on V , find an ordered basis for the T -cyclic subspace generated by the vector v.

(a) V =R3,T(a,b,c)=(2a+b,b−3a+c,4c)wherev=(1,0,0).

(b) V = P3(R), T(f(x)) = 3f′′(x), and v = x2.

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