\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For each of the following subsets of \(\mathbb{R}^2\), say whether it is a subspace.
  1. \(F_1 = \{(x, y) \in \mathbb{R}^2 : x = y\}\).
  2. \(F_2 = \{(x, y) \in \mathbb{R}^2 : 2x - 5y - 1 = 0\}\).
  3. \(F_3 = \{(x, 2x) : x \in \mathbb{R}\}\).
  4. \(F_4 = \{(x, y) \in \mathbb{R}^2 : x^3 + x + y^2 = 0\}\).

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