(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 = R^{4}, T(a+b,b-c,a+c,a+d) and z= e_{1}

2. Relevant 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), T^{2}(v),..., T^{k-1}(v)} is a basis for W.

3. The attempt at a solution

v= (1,0,0,0), T(v)= (1,0,1,1), T^{2}(v)= T(T(v))= (1,-1,2,2), T^{3}(v)= T(T^{2}(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)} ?

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# Homework Help: T-Cyclic Subspaces

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