السلام عليكم
ذَهَبْتُ إِلَى بَيْتِ الرّجُلِ الكَبِيرِ
Translation: 1).'I went to the house of the old/great man' or 2).'I went to the large house of the man.'
Ok, here are my thoughts:
Firstly, ذَهَبْتُ (I went) could have been ذَهَبَتِ (You went first person feminine) ذَهَبَتَ (You went first person masculine) or ذَهَبَتْ (She went)
However, for the female to go in this context (i.e. to the house of the man) seems inappropriate but is nonetheless plausible, just as the first person m/f is also probable, but to avoid dispute, I left it as 'I' so that the first person can represent masculine or feminine.
Translation 1 reason for vowelisation: The man in relation to the بَيْتِ is its possesor, and therefore, in the genetive case and also definite. This means that any adjective of the man will have to follow in case, definition, number and gender as well. Thus, الكَبِبرِ fits into this category and can therefore continue in the genetive case after الرّجُلِ.
Translation 2 reason for vowelisation: Even in the second translation, the vowelling stays the same. This is because the adjective of بَيْتِ must be masculine, singular, genetive and definite as the word بَيْتِ engenders all these. Also the possessed (بَيْتِ)has been rendered definite by the possesor in the إضافة construction i.e. the ال on the possessor الرّجُلِ has made the word بَيْتِ definite.
Also, the reason why translation number 2 can work is because, the adjective الكَبِبرِ is placed after the possessor because it is not allowed to come in between the possessive construction: 'بَيْتِ الرّجُلِ'
Finally, all the cases have been rendered genetive due to the preposition إِلَى at the beginning.
مع السلامة