\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
For each of the following vector spaces, decide whether it is of finite dimension. Justify briefly.
  1. \(E_1 = \mathbb{R}^5\).
  2. \(E_2 = \mathbb{R}_4[X]\) (polynomials of degree \(\le 4\)).
  3. \(E_3 = \mathcal{M}_{2,3}(\mathbb{R})\).
  4. \(E_4 = \mathbb{R}[X]\) (all polynomials).

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