Q1: What is the area of the parallelogram spanned by the vectors $ \begin{pmatrix} 2 \ 1 \end{pmatrix}$ and $ \begin{pmatrix} -1 \ 1 \end{pmatrix}$?

A1: 3

A2: 2

A3: -3

A4: 4

A5: -4

Q2: What is the orientated area of the square spanned by $ \begin{pmatrix} 0 \ 2 \end{pmatrix}$ and $ \begin{pmatrix} 2 \ 0 \end{pmatrix}$?

A1: -4

A2: -2

A3: 2

A4: 4

A5: 0

Q3: Assume $\mathrm{vol}_2(\mathbf{u}, \mathbf{v}) = 0$. Are the vectors $\mathbf{u}, \mathbf{v}$ linearly dependent?

A1: Yes, always.

A2: No, never. They are linearly independent.

A3: No, they are counterexamples.

A4: Yes, but only if one assumes that both vectors are non-zero.

A5: One needs more information.