1. Mother Teresa helped many people in India.
(In this sentence, what is the part of speech of 'in India?' Is it an adverbial phrase modifying 'helped' or is it an adjective phrase which modifies 'people?')
2. You watched The Matrix yesterday.
3. You watched the Matrix yesterday.
(Which one is right,'The' or 'the?' I think 'The Matrix' is a movie title, right?)
1. It's an adjective phrase (adjectival prepositional phrase) modifying "people," yes.
2. The Matrix is correct. Since it's a movie title, you need to put it in italics or underline those two words. Poems, short stories, and such have quotation marks around them, but book titles, movie titles, titles of artwork, and others need to be italicized or underlined.
1. In the sentence, "in India" is an adverbial phrase modifying the verb "helped." It provides additional information about where Mother Teresa's assistance took place.
2. Both sentences are grammatically correct, but they have different meanings. "You watched The Matrix yesterday" implies that you watched a specific movie titled "The Matrix." "The Matrix" is indeed a movie title, and the use of "The" indicates that it is referring to a specific movie.
3. On the other hand, "You watched the Matrix yesterday" suggests that you watched a movie called "Matrix" without specifying if it is "The Matrix" or another movie with a similar name. In this case, "the" is used as a definite article, indicating that the noun ("Matrix") is something previously mentioned or known to both the speaker and the listener.