I saw that one eats a kzayis from the whole matza, and a kzayis from the broken matza. One reason given is because one is supposed to eat from the matza that hamotzi was said on and also eat from the mata that the bracha of matza was said on. I am trying to understand: When one makes a bracha on food, does he make the bracha on a specific piece of food that he needs to eat from? Also, when one makes a bracha on a mitzvah, does he make a bracha on a specific item? And why would he need to either taste from or eat a kzayis from the matza that the bracha of matza was said on? Thank you very much, Yitzchok
The OP's first question was:
When one makes a bracha on food, does he make the bracha on a specific piece of food that he needs to eat from?
See here for a relevant discussion. It is clear from there that the bracha goes on the specific food I am planning on eating. There is a machlokes regarding the rest of the food, as mentioned there.
We also see from Y.D. 19, regarding the laws of making the bracha over shechita, that the halachos are basically similar and we learn the halachos of blessing over food from blessings over mitzvos and vice versa.
It's also assumed that the one making the bracha will be eating from that upon which he is making the bracha. If he is exempting others, however, they do not need to eat from his item. This is clear from Shulchan Aruch O.C. 167:15. If one person is making hamotzei for multiple people, and they are all planning on eating from his bread, then he needs to eat first. But if they all have their own bread, and he is just exempting them in the bracha, then they can eat after he blesses even before he himself eats from his bread. There is no obligation for them to eat from his bread, though some say it is meritorious.
Regarding the question eating a kezayis, look at O.C. 475:1 with the Mishna Berurah. There's a mitzvah to eat a kezayis of matzah since the mitzvah is "to eat" matza, and the minimum quantity of "eating" with halachic significance is a kezayis. The M.B. there points out that technically, the bracha of hamotzi only requires a small little bit. The Beur HaGra points out that according to some opinions, eating both quantities from the same matzah would violate the principle of "Ein Osim Mitzvos Chavilos Chavilos", we don't want to use the same item to fulfill multiple obligations simultaneously. Although it is not clear that the principle would apply here, we use multiple matzos to avoid the controversy.
However, we have a further doubt regarding which matzah to use for which mitzvah. We know that we take two matzos, the top whole matzah and the middle broken matzah (the bottom matzah is only for lechem mishna purposes and doesn't matter for this.) One matzah is for the mitzvah of eating matza (which requires a kezayis) and the other is for hamotzei (and only requires a bit). But since there's a machlokes which matza is for which purpose, it's proper to have a kezayis from each matza to fulfill both opinions. (Strictly speaking, it's only obligatory to have a kezayis from the middle matzah, since the halacha follows the opinion that the middle matza is for the mitzva).