How do I know if this is a linear combination

ok so I have
(1,2,3) = a(2,2,2) + b(1,0,1)

I am trying to find out if (2,2,2) and (1,0,1) are linear combinations of (1,2,3). Cant remember though how to tell if it is or isnt. So I need to know if a and b exist such that they can make (1,2,3) and are hence a linear combination.

Help on how to do this would be greatly appreciated, thanks.

You would have to satisfy

2a + b = 2
2a = 2
2a + b = 3

No solution!