Question: Problem 8. (20 points.) Consider the operator S on the vector space Ri[x] given by S(atbr) = -a+b+ (a+2b)x (8A) Pick a basis B =

Problem 8. (20 points.) Consider the operator S on the vector space Ri[x] given by S(atbr) = -a+b+ (a+2b)x (8A) Pick a basis B = {b1, by}. Find the minimal polynomials, ur, , (y), AT,b, (y), and us(y). (8B) Show that S is cyclic by finding a vector v such that (S, v) = Ri[x]. (8C) Is S irreducible? (8D) Is S indecomposable

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