Which maps of three-space are linear

Let the mappings $T_1,T_2,T_3,T_4$ from $\mathbb R^3$ to $\mathbb R^3$ be defined by

$$T_1(x,y,z)=(x^2+y^2, x+z, x+y+z);$$

$$T_2(x,y,z)=(y+z, z+x, x+y);$$

$$T_3(x,y,z)=(x+y, xy, x-z);$$

$$T_4(x,y,z)=(x, 2y, 3z).$$

Then which of these are linear transformations of $\mathbb R^3$ over $\mathbb R$?