I would imagine you would assign each multiple choice answer a value of 0 or 1, based on whether they selected that answer or not. So if there was just one ques

I would imagine you would assign each multiple choice answer a value of 0 or 1, based on whether they selected that answer or not. So if there was just one question, and the student answered 'A', it would produce a vector like [1, 0, 0, 0]. In fact I believe there are similar but better algorithms than PCA for handling mutually exclusive binary variables. I just don't know what they are called.