A change of basis

Suppose we have two bases from a vector space $\mathbb{R}^3$: $e_1 = (1, 1, 1)$, $e_2 = (-1, 1, 0)$, $e_3 =( 2, -2, -2)$ and $e'_1 = (3, -3, -2)$, $e'_2 = (3, 1, -2)$, $e'_3 =( 1, 3, 0)$, and the transition matrix from $\mathbf{e}$ to $\mathbf{e'}$ is $\begin{pmatrix} 0 & 2 & 2\\ -1 & 3 & 3\\ 1 & 2 & 1 \end{pmatrix}$. The coordinates of a vector $v$ in basis $\mathbf{e}$

are $\begin{pmatrix} -4 \\ -4 \\ -5 \end{pmatrix}$. What coordinates does the vector $v$ have in the basis $\mathbf{e'}$?

The options are:

1) $\begin{pmatrix} -2 \\ -1 \\ -1 \end{pmatrix}$;

2) $\begin{pmatrix} -18\\ -23 \\ -17 \end{pmatrix}$;

3) This is not a transition matrix from $\mathbf{e}$ to $\mathbf{e'}$;

4) $\begin{pmatrix} -4 \\ -4 \\ -5 \end{pmatrix};$

Tip: Matrix inverse to the transition matrix from $\mathbf{e}$ to $\mathbf{e'}$ is $C^{-1} = \begin{pmatrix} 1.5 & -1 & 0 \\ -2 & 1 & 1 \\ 2.5 & -1 & -1 \end{pmatrix}.$