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SOLVED: On which of the following domains, given in interval notation, would the restriction of f(r) be one-to-one? Select all correct answers.(-2, 0.21)[-6, -2][-5, -1][-6, 0.21][1, 5] U [2][-3, 0]
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SOLVED:Let T̂ denote the restriction of an operator T to an invariant subspace W. Prove (a) For any polynomial f(t), f(T̂)(w)=f(T)(w) (b) The minimal polynomial of T̂ divides the minimal polynomial of T (a) If f(t)=0 or if f(t) is a constant (i.e., of degree 1 ), then the result clearly holds. Assume deg f=n>1 and that the result holds for polynomials of degree less than n. Suppose that Then f(t)=an t^n an-1 t^n-1 ⋯ a1 t a0 f(T̂)(w) =(an T̂^n an-1 T̂^n-1 ⋯ a0 I)(w) =(an T̂^n-1)(T̂(w
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