\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Write the \(3 \times 3\) matrix realizing each of the following row operations: (1) the swap \(L_1 \leftrightarrow L_3\); (2) the scaling \(L_2 \leftarrow -5 L_2\); (3) the transvection \(L_3 \leftarrow L_3 - 2 L_2\).
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