Solution Found!
Let V andW be vector spaces (not necessarily finite-dimensional), and let T : V W be a
Chapter 4, Problem 11(choose chapter or problem)
Let V and W be vector spaces (not necessarily finite-dimensional), and let \(T:\ V\ \rightarrow\ W\) be a linear transformation. Check that ker\((T)\ \subset\ V\) and image \((T)\ \subset\ W\) are subspaces.
Questions & Answers
QUESTION:
Let V and W be vector spaces (not necessarily finite-dimensional), and let \(T:\ V\ \rightarrow\ W\) be a linear transformation. Check that ker\((T)\ \subset\ V\) and image \((T)\ \subset\ W\) are subspaces.
ANSWER:Problem 11
Let V and W be vector spaces (not necessarily finite dimensional) and let 
Step by Step Solution
Step 1 of 2
Given that V and W be vector spaces (not necessarily finite dimensional) and let
By definition,
Now, it is clear that 
Also, the definition is independent of the dimension of V and W.