At my school I have learned - linking verbs are followed by adjectives but the following sentences confuse me.
He is a good teacher.
He became headmaster.
She is a nurse.
In the above sentences Linking verbs are followed by noun and noun phrase.
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I am going to answer your implicit question, which is 'how can this happen?'
The answer is that 'linking verbs' can be followed by adjectives or nouns. In the cases you cite, it is nouns.
The following sentences use adjectives or nouns.
The teacher is good (adjective)
He is a teacher (noun)
The nurse felt sick (adjective)
The nurse felt the broken leg (noun)
You are going to be able (usually) to spot the noun by the use of an article.
"Linking verbs" or "copulative verbs" are used in TWO ways:
Subject + verb + noun (or noun phrase)
Subject + verb + adjective ( or adjectival phrase)
What is not grammatical is:
Subject + verb + adverb
Now of course a noun phrase or adjectival phrase may contain an adverb modifying an adjective.
Tom is slightly
is so grossly ungrammatical as to have no discernible meaning.
Tom is slightly obese
is grammatical, but "slightly" modifies "obese," and the entire adjectival phrase describes Tom.