Let x = [x1 x2 x3 x4]T with "T" meaning transpose.
Ax = 0 gives
x1 - 4x2 + 5x3 + 4x4 = 0 and
2x1 - 8x2 + 10x3 + 8x4 = 2(x1 - 4x2 + 5x3 + 4x4) = 0
There is only 1 independent equation describing x and it describes a plane in R4: x1 - 4x2 + 5x3 + 4x4 = 0.