GATE 2018 | MATHS | Q-24

Question

Consider the subspaces
\[ W_1 = \{(x_1, x_2, x_3) \in \mathbb{R}^3 : x_1 = x_2 + 2x_3 \} \]
\[ W_2 = \{(x_1, x_2, x_3) \in \mathbb{R}^3 : x_1 = 3x_2 + 2x_3 \} \]
of \( \mathbb{R}^3 \). Then the dimension of \(W_1 + W_2\) equals_________