Determine whether the set \(\left\{ \begin{bmatrix}2\\1 \\1\…
Determine whether the set \(\left\{ \begin{bmatrix}2\\1 \\1\end{bmatrix}, \begin{bmatrix}1\\-1 \\4\end{bmatrix}, \begin{bmatrix}0\\2 \\3\end{bmatrix}\right\}\) forms a basis for \(\mathbb{R}^3\).