A transformation, T, is "linear" if and only if T(u+ v)= T(u)+ T(v) and T(av)= aT(v) for u and v vectors and a a number.

For example, for A, T(x1,x2,x3)= (8, 7, 2) no matter what "x1", "x2", or "x3" are. So T(ax1, ax2, ax3)= (8, 7, 2) also. Is that the same as aT(x1,x2,x3)?

For B, T(x1)= (6x1, 5) so T(ax1)= (6ax1, 5). Is that the same as aT(x1)?