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Here is my question.

A is a 4x4 matrix and there are two vectors, b and c, which have 4 real numbers. If we are told that A(vector x)=(vector b) has an unique solution, how many solutions does A(vector x)=(vector c) have?

I honestly have no idea how to do this. I know that for A would be in the following rref form:

1 0 0 0

0 1 0 0 for Ax=b.

0 0 1 0

0 0 0 1