Find the transformation is linear and determine whether the transformation is an isomorphism.
The solution is that T is a liner transformation and not an isomorphism.
Consider two linear spaces V and W. A function T is said to be linear transformation if the following holds.
For all elements f,g of V and k is scalar.
A linear transformation is said to be an isomorphism if and only if and or .
The given transformation as follows.
, from V to V.
By using the definition of linear transformation as follows.
Now, to check the first condition as follows.
Consider two infinite sequences V from as follows.
and be an infinite sequences from V.
Now, simplify as follows.
Simplify for the second condition as follows.
Thus, T is a linear transformation.
A linear transformation is isomorphism if and only if and
Now, it easy to show that and .
That is the inverse of role="math" localid="1659416754005" does not have unique vector to map to.
This means that T is not an isomorphism.
Thus, T is a linear transformation and not an isomorphism.
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