The vectors $v_1 = \begin{bmatrix} 1 \\ -2 \end{bmatrix}$, $v_2 = \begin{bmatrix} 4 \\ -13 \end{bmatrix}$, $v_3 = \begin{bmatrix} -1 \\ -3 \end{bmatrix}$ span $R^2$ but do not form a basis. Find two different ways to express $\begin{bmatrix} -10 \\ 35 \end{bmatrix}$ as a linear combination of $v_1, v_2, v_3$.
Write $\begin{bmatrix} -10 \\ 35 \end{bmatrix}$ as a linear combination of $v_1, v_2, v_3$ when the coefficient of $v_3$ is 0.
$\begin{bmatrix} -10 \\ 35 \end{bmatrix} = \begin{bmatrix} 1 \\ -2 \end{bmatrix}v_1 + \begin{bmatrix} 4 \\ 13 \end{bmatrix}v_2$