8. Consider the vector space V₃ spanned by the four vectors

$$

\mathbf{v}_1 =

\begin{bmatrix}

2 \\

-1

\end{bmatrix};

\mathbf{v}_2 =

\begin{bmatrix}

1 \\

0

\end{bmatrix};

\mathbf{v}_3 =

\begin{bmatrix}

4 \\

-1

\end{bmatrix};

\mathbf{v}_4 =

\begin{bmatrix}

-1 \\

1

\end{bmatrix}.

$$

and consider the transformation A where

$$

\mathbf{A} =

\begin{bmatrix}

1 & 0 & 2 \\

-1 & -1 & 3 \\

-1 & 2 & 4

\end{bmatrix}.

$$

If each vector in V₃ is transformed by A, then by Theorem 3.1.1, the resulting set of vectors is a vector space which we shall denote by S₃. Is the voulu x' = [1, 1, -1] in S₃?