7. Suppose that T : V ! V is a linear transformation. Show that N(T) is a subspace of
N(T^3), and R(T^3) is a subspace of R(T). Show also that N(T) = N(T^3) if and only if
R(T) = R(T^3)
Can any1 solve this?
Follow Math Help Forum on Facebook and Google+
For , consider and calculate: .
For , consider . Then for some . Letting we see that , so .
For the last sentence, observe that and . So equating one subspace with the other, means that their respective direct complements are equal.
View Tag Cloud