Determine the matrix of the linear mapping $L$ with respect to the basis $B = \begin{Bmatrix} \begin{bmatrix} 0 \\ 1 \\ 1 \end{bmatrix}, \begin{bmatrix} -2 \\ 1 \\ 2 \end{bmatrix}, \begin{bmatrix} -2 \\ 0 \\ 2 \end{bmatrix} \end{Bmatrix}$, where \\
$[L(0, 1, 1)]_B = (3, 0, 0)$, $[L(-2, 1, 2)]_B = (0, 1, 0)$, $[L(-2, 0, 2)]_B = (0, 0, 0)$