Let \(A=\begin{bmatrix}|&|&|\\\vec {c}_1& \vec {c}_2 & \vec {c}_3\\|&|&|\end{bmatrix}\) be a \(3\times 3\) matrix with columns \(\vec {c}_1\), \(\vec {c}_2\) and \(\vec {c}_3\).

Suppose \(A\begin{bmatrix}-1\\-1\\2\end{bmatrix}=\begin{bmatrix}0\\1\\1\end{bmatrix}\)

Which of the following can we conclude from the given information? Select ALL that apply.

\(\vec {c}_2+\vec {c}_3=\begin{bmatrix}-1\\-1\\2\end{bmatrix}\) \(-\vec {c}_1-\vec {c}_2+2\vec {c}_3=\begin{bmatrix}0\\1\\1\end{bmatrix}\) \(A\) is non-singular. \(\begin{bmatrix}0\\1\\1\end{bmatrix}\) is in \(\text {span}(\vec {c}_1, \vec {c}_2, \vec {c}_3)\). Vector \(\begin{bmatrix}0\\1\\1\end{bmatrix}\) can be written as a linear combination of the columns of \(A\).