Assume that $T$ is a linear transformation $T: V → ℝ$ and $T(\mathbf{v}_1)=1$ , $T(\mathbf{v}_2)=-1$, find $T(3\mathbf{v}_1-5\mathbf{v}_2)$ Assume that $T$ is a linear transformation $T: V\to\mathbb{R}$ 
$T(\mathbf{v}_1)=1$, $T(\mathbf{v}_2)=-1$
find  $T(3\mathbf{v}_1-5\mathbf{v}_2)$
Not sure how to go about this question

As $T$ is a linear transformation, we have:
$$T(3v_1-5v_2)=T(3v_1)-T(5v_2)=3T(v_1)-5T(v_2)=3\cdot1-5\cdot-1=3+5=8$$
