Let be

.

What is the rank of A and [A|b] expanded matrix over GF(2), GF(3) and (where GF(2) and GF(3) are the Galois fields of two/three elements and R means real numbers).

What can we say we about the solvability of Ax=b system of linear equations in the three cases (GF(2), GF(3), R)?

I would be very grateful, if you could help me!

Thank you!