Question: no data missing, complete question, please do not juest leave incomplete question 6. Let V = R4, T : V be defined by T(a, b,

no data missing, complete question, please do not juest leave incomplete question

6. Let V = R4, T : V be defined by T(a, b, c, d) = (a + b + c, b + 2c-d,c+ 2d, -2d), and 2 = 63. (a) Find an ordered basis for the T-cyclic subspace W of V generated by z. (b) Let W be the T-cyclic subspace found in (a), find the characteristic polynomial fw(t) of Tw in two ways. Find the characteristic polynomial f (t) of T. (c) Show that fw(t) divides f(t), that is, f(t) = fw(t)g(t), where g(t) is some polyno- mial

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