A set of two, three, or four red vectors in $\mathbb{R}^2$ or $\mathbb{R}^3$ is shown in each picture below. Determine whether each set of vectors is a basis for $\mathbb{R}^2$ or $\mathbb{R}^3$. Note: For the pictures in $\mathbb{R}^3$, a grid is drawn in the $xy$-plane, and vectors with their tip on the grid are in the $xy$-plane, while vectors with their tip not on the grid are not in the $xy$-plane.

choose basis not a basis		choose basis not a basis		choose basis not a basis
choose basis not a basis		choose basis not a basis		choose basis not a basis