Answer
See below
Work Step by Step
We obtain:
$(T_2T_1)v=T_2(T_1(v))\\
=T_2(T_1(\alpha v_1 + \beta v_2))\\
=T_2(\alpha T_1( v_1)+\beta T_1(v_2))\\
= T_2(\alpha (3v_1+v_2)+\beta (0))\\
=T_2(3\alpha v_1+\alpha v_2)\\
=3\alpha T_2 (v_1)+\alpha T_(2v_2\\
=3\alpha (-5v_2)+\alpha(-v_1+6v_2)\\
=-15\alpha v_2-\alpha v_1+6\alpha v_2\\
=-\alpha v_1-9\alpha v_2\\
=-\alpha(v_1+9v_2)$
for $v=\alpha v_1 +\beta v_2$
