\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Compute the rank of each of the following families:
  1. \(\bigl((1, 2, 3), (2, 4, 6), (3, 6, 9)\bigr)\) in \(\mathbb{R}^3\).
  2. \(\bigl((1, 0, 1), (0, 1, 1), (1, 1, 2), (1, -1, 0)\bigr)\) in \(\mathbb{R}^3\).
  3. \(\bigl(1 + X, 1 - X, X^2, 1 + X^2\bigr)\) in \(\mathbb{R}_2[X]\).

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