Q1: On $\mathbb{R}^2$ we have two operations. How is the addition defined?

A1: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 \ v_2 \end{pmatrix} $$

A2: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1+ w_1 \ v_2 +w_2 \end{pmatrix} $$

A3: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 w_1 \ v_2 w_2 \end{pmatrix} $$

A4: $$ \begin{pmatrix} v_1 \ v_2 \end{pmatrix} + \begin{pmatrix} w_1 \ w_2 \end{pmatrix} = \begin{pmatrix} v_1 \ v_1 \end{pmatrix} $$

Q2: On $\mathbb{R}^2$ we have two operations. How is the scalar multiplication defined?

A1: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ v_2 \end{pmatrix} $$

A2: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} v_1 \ \lambda v_2 \end{pmatrix} $$

A3: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ \lambda v_2 \end{pmatrix} $$

A4: $$ \lambda \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix} = \begin{pmatrix} \lambda v_1 \ \lambda v_2 v_1 \end{pmatrix} $$

Q3: What is $$5 \cdot \begin{pmatrix} 1 \ 2 \end{pmatrix} + \begin{pmatrix} 0 \ 1 \end{pmatrix} \text{?}$$

A1: $$\begin{pmatrix} 5 \ 10 \end{pmatrix}$$

A2: $$\begin{pmatrix} 6 \ 10 \end{pmatrix}$$

A3: $$\begin{pmatrix} 6 \ 11 \end{pmatrix}$$

A4: $$\begin{pmatrix} 5 \ 11 \end{pmatrix}$$

A5: $$\begin{pmatrix} 6 \ 12 \end{pmatrix}$$