Can basis vectors have fractions? So I was diagonalizing a matrix in a book, and one of the basis vectors was [3/2, 1], after doing the problem, the answer in the book was different than mine. It came with an explanation, and in it the basis vector was [3,2]. They are the same thing, just multiples of each other, so I was curious, is it mandatory to take fractions out of a basis vector?

You are right and they are also right. This is because multiplication by non-zero constants does not affect the span of the basis nor the linear independence of the vectors in that basis. You should be able to see this quite obviously once you think about it.
