The sum of any two vectors $$\color{vred}\overrightarrow{v}$$ and $$\color{vblue} \overrightarrow{w}$$ results in a third vector$$\color{vgreen} \overrightarrow{z}$$. The components of $$\color{vgreen} \overrightarrow{z}$$ are the sum of $$\color{vred}\overrightarrow{v}$$ and $$\color{vblue} \overrightarrow{w}$$ components.
$$\color{vred}\overrightarrow{v} + \color{vblue}\overrightarrow{w} \color{black} = \color{vgreen} \overrightarrow{z}$$
$$\color{vred} \begin{bmatrix} v_1 \\ v_2 \\ \vdots \\ v_n \end{bmatrix} + \color{vblue} \begin{bmatrix} w_1 \\ w_2 \\ \vdots \\ w_n \end{bmatrix} = \color{vgreen} \begin{bmatrix} z_1 \\ z_2 \\ \vdots \\ z_n \end{bmatrix}$$
$$\color{vgreen}\overrightarrow{z} = \begin{bmatrix} {\color{vred}v_1} + {\color{vblue}w_1} \\ {\color{vred}v_2} + {\color{vblue}w_2} \\ \vdots \\ {\color{vred}v_n} + {\color{vblue}w_n} \end{bmatrix}$$
$$\begin{bmatrix} 1 \\ 1 \end{bmatrix} + \begin{bmatrix} 1 \\ 2 \end{bmatrix} = \begin{bmatrix} 2 \\ 3 \end{bmatrix}$$
$$\begin{bmatrix} -1 \\ 0 \end{bmatrix} + \begin{bmatrix} 2 \\ -1 \end{bmatrix} = \begin{bmatrix} 1 \\ -1 \end{bmatrix}$$