For which conditions on b=(b1​,b2​,b3​,b4​) do there exist solution(s) for the linear system Ax=b ?

(a) A= [ 1 2 3 1 ]
[ 6 12 12 10 ]
[ 4 8 14 16]

(b) B= [1 1 1 1 1 1 1]
[2 2 4 4 6 6]