Question: 5.15 Example Define an operator T = L(F2) by T(x, y) = (y,0). Let U = {(x,0): x F}. Show that (a) (b) (c)

5.15 Example Define an operator T = L(F2) by T(x, y) =

5.15 Example Define an operator T = L(F2) by T(x, y) = (y,0). Let U = {(x,0): x F}. Show that (a) (b) (c) U is invariant under T and Tlu is the 0 operator on U; there does not exist a subspace W of F2 that is invariant under T and such that F2 = U+W; T/U is the 0 operator on F2/U.

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