It's fine grammatically. There is no need for the 'only' - the word exclusively makes that clear. This is called 'tautology' and is considered a little messy.
the word exclusively is an adverb right? and it's a modifier. and adverb only modifies a verb, an adjective and another adverb. in hte sentence the adverb is follwed by the preposition for. I'm thinking if exclusively be replaced by the word "exclusive" instead. what do u think?
But "is" is a linking verb. And after any linking verb there's the predicate adjective or predicate nominative only but not predicate adverb? Maybe I missed it but is there any grammar rule that sez adverb can modify linking or auxiliary or helping verbs like "is"? Please help.
Any word that modifies a verb is an adverb. It doesn’t matter if it’s a linking verb or an action verb: what matters is that a verb is being modified.
Study the following examples:
1. The singer sings beautifully.
“Well” is an adverb because it describes the verb “sings”.
2. The singer is beautiful.
“Good” is an adjective because it modifies “the singer,’ not “is”.
3. The singer is here.
“Here” is an adverb because it describes where she is, not what kind of singer she is.
I suppose you could have spoken differently, and called the area “exclusive“ but you didn't, and that's ok, because instead, you described how the area is for the students: exclusively for them. that's why your sentence was grammatically correct.
I think you're looking too hard. You obviously have an excellent grasp of grammar. I have found that the more you (one - if you're still in the 19th century) know about grammar, you better you can justify errors.
'Exclusively' definitely modifies 'is' in your sentence. No question.
e.g. Sarah is in charge from 7 o'clock.
'from o'clock' is an adverb of time modifying 'is'. It could equally have gone at the front (with a comma usually - not essential).
Yes, the problem with the rule as you state it is the word "after". The truth is you can use an adjective "after" a linking verb, but not to modify one. In English, just because a word comes after another doesn't always tell you what it's doing there. You have to see what the word is doing, not where it is. This is the difference between simple "word order" and "syntax".
Languages like Latin don't even use word order much to show the syntax, they use "cases" like we could do with the words "I" and "me". I.e., in Latin, you could say "she me saw" or "me she saw" or "saw me she" or whatever because it's the case that shows you the syntax, not the word order.