\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Write the \(3 \times 3\) matrix \(E\) realizing the transvection \(L_2 \leftarrow L_2 + 3 L_1\) (i.e.\ such that for every \(A \in M_{3, p}(\mathbb{R})\), the matrix \(E A\) equals the matrix obtained from \(A\) by this row operation). Verify on \(A = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 4 & 1 \\ 2 & 3 & 0 \end{pmatrix}\).
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