1. Show that the three vectors

$$e_1 = \begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}$$; $$e_2 = \begin{bmatrix} 0 \\ 1 \\ 0 \end{bmatrix}$$; $$e_3 = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}$$

are a basis for R3.