Solution

We could just ask for the rank, but show human arguments below! We start row reducing to determine rank.

Apply Gauss elimination

Thus the rank is 2. Let us think columns and say that the column space has rank 2, or a basis of two vectors. If we change one of the entries, then it is like removing one of the vectors and replacing it with one new vector. To make the rank 4, we need two new vectors! So, this is not possible.

Here is a more convincing way of saying it!
When we drop a vector from a spanning set of a two dimensional space, the resulting space can be either one or two dimensional. (It simply depends on whether the remaining vectors contain a basis or not). Another way of saying this is that when we drop one of vectors from a spanning set, the remaining vectors span a subspace, so its dimension is at most 2.
Now, when we add one new vector, the dimension can jump by no more than 1. So the rank of can be jacked up to 3 but not to 4!