Question: Let X, Y be the two vector spaces over the same field F and T:X-Y is a function such that Tax+by) = aT(x)+bT(y). Then (1)

Let X, Y be the two vector spaces over the same field F and T:X-Y is a function such that Tax+by) = aT(x)+bT(y). Then (1) R(T) = T(X) = {T(x): XE X} is subspace of Y. (i) N(T)=Ker (T)={x X: T(x)=0 } is a subspace of X.

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