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

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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

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