\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the family \((E_{11}, E_{12}, E_{21}, E_{22})\) in \(M_2(\mathbb{R})\) is linearly independent, i.e.\ if \(\alpha E_{11} + \beta E_{12} + \gamma E_{21} + \delta E_{22} = 0\) then \(\alpha = \beta = \gamma = \delta = 0\).
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