Prove whether or not these functions are linear transformation.

a) $\displaystyle F:V_3(R) \to V_2(R),$ defined by $\displaystyle F(a_1, a_2, a_3)=(a_1+a_2, a_1a_3-a_2)$

b) $\displaystyle G:V_3(R) \to V_2(R),$ defined by $\displaystyle G(a_1, a_2, a_3)=(a_1-a_2, 2a_1-a_3)$