Question

Which of the following does not give a subspace of \(\mathbb{R}^2\)?

1. \(\left \{ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}: x_1^2 = 0 \right \}\)

2. \(\left \{ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}: 2x_1 = x_2 \right \}\)

3. \(\left \{ \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}: |x_1|+|x_2| = 2 \right \}\)