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hitmeoff
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Homework Statement
For each linear operator T on the vector space V, find an ordered basis for the T-Cyclic subspace generated by the vector z.
a) V = R4, T(a+b,b-c,a+c,a+d) and z= e1
Homework Equations
Theorem: Let T be a linear operator on a finite dimensional vector space V, and let W denote the T-cyclic subspace of V generated by a nonzero vector v [tex]\epsilon[/tex] V. Let k = dim(w). Then:
a) {v, T(v), T2(v),..., Tk-1(v)} is a basis for W.
The Attempt at a Solution
v= (1,0,0,0), T(v)= (1,0,1,1), T2(v)= T(T(v))= (1,-1,2,2), T3(v)= T(T2(v)) = (0,-3,3,3)
so basis for W = {(1,0,0,0), (1,0,1,1), (1,-1,2,2), (0,-3,3,3)} ?