Rutherford's Gold Foil Experiment - Why did they think that the stream of alpha particles would pass through? Why did Rutherford think that the alpha particles would pass straight through the gold foil with minor deflections based on Thomson's model?
Since Thomson believed that the atoms consists of a positive matrix with electrons floating in it, shouldn't majorly all of the alpha particles deflect off the gold foil from the repulsion of like charges and only the rays that hit the electrons should pass through? (I know this is not actually what happens but I just don't understand why they thought this)
 A: To lay some groundwork, Thomson's model assumed that there was a positive matrix (as you say) encapsulating the floating electrons in order for the overall charge to be neutral. In this reference alpha particles that go through the nucleus should not be deflected greatly, as they flow through with little repulsion due to a small density.
Where I think that you're confused is the absolute repulsion of the surrounding positive matrix. Because the positive matrix is supposed to encapsulate all of the electrons, its overall density would be much less than that of the Rutherford model. Rutherford's model found that there was a high density in the centre, with the electrons floating around it. Taking both of these into account, Thomson's model took the idea of a positive (low density) charge encapsulating electrons that would create little repulsion due to its much larger size compared to Rutherford's model. While Rutherford's model found that this was incorrect as the high density of the atom repelled the alpha particles at more varied rates than what would be expected of one of Thomson's models.
To expand upon these models, you can think of Rutherford's in terms of poorly cooked boba pearls, and Thomson's as perfectly cooked boba pearls. This meaning that the outside is soft and squishy while the inside is hard, and the other being perfectly smooth and easy to chew, with each respectively. If you were to think of your bite as the path that the alpha particles would take, it would rebound from the poorly cooked boba, while it would go straight through with the well-cooked boba.
I hope this makes sense, feel free to leave any comments if I got something incorrect or you want to expand on anything that I have said.
