Question: 2. Suppose V is a nite dimensional vector space and T : V > V is a linear operator satisfying 1'2 = T + 121},

2. Suppose V is a nite dimensional vector space and T : V > V is a linear operator satisfying 1'"2 = T + 121}, where IV : V > V is the identity operator. (a) Let E_3 = {v E V : T(v) = 3v} and E4 = {v E V : T(v) = 4v} be the [3) and (4)eigenspaces, respectively. Show that V = E_3 e: E4. 4v T(v) 3v + T(v) H't:W't :+ m riev 7 7 (b) Show that there is a basis 3 for V such that [T] 3 has the blockdiagonal form mm\"): [its til for some choice of m, n E N

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