Answer
$T(x) = c_1T(v_1)+...+c_pT(v_p) = c10+...+c_p0 = 0$
Work Step by Step
Given any x in $R^n$, there are constants $c_1,...,c_p$ such that $x= c_1v_1+ ... c_pV_p$ because $v_1,...,v_p$ span $R_n$. Thus, using property(5) of a linear transformation.
