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Is it a necessary for a Linkng Verb to be an intrasitive verb.

For Example. Take the verb "feel".

1. The blanket feels soft, warm and comfortable.

2. The child felt the blanket.

GB
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Linking verbs are not always considered intransitive verbs (there are generally 3 types listed: transitive, intransitive, and copular); but they do not take an object-- when acting as a linking verb. I say this because your examples are of a verb that can be either transitive, intransitive, or copular, depending on the meaning:

I feel my nose.
I feel for you.
I feel hungry
.
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Wonderful examples!
Sometimes the verb "feel" is intransitive, as in "I feel bad." In this case, it is a sense of being, not a physical act of touching something. Therefore, you would use the predicate adjective "bad" as opposed to the adjective "badly." This is a very, very common mistake.