2. Determine whether the following sets form sub-
spaces of \(\mathbb{R}^3\):
(a) \(\{(x_1, x_2, x_3)^T \mid x_1 + x_3 = 1\}\)
(b) \(\{(x_1, x_2, x_3)^T \mid x_1 = x_2 = x_3\}\)
(c) \(\{(x_1, x_2, x_3)^T \mid x_3 = x_1 + x_2\}\)
(d) \(\{(x_1, x_2, x_3)^T \mid x_3 = x_1 \text{ or } x_3 = x_2\}\)