The problem asks to identify the element $a_{12}$ of the given matrix $A$. The matrix $A$ is given as: $A = \begin{bmatrix} 1 & 0 & -2 \\ 3 & 2 & 1 \\ 4 & 0 & 3 \end{bmatrix}$

1. Problem Description

The problem asks to identify the element $a_{12}$ of the given matrix $A$. The matrix $A$ is given as:

$A = \begin{bmatrix} 1 & 0 & -2 \\ 3 & 2 & 1 \\ 4 & 0 & 3 \end{bmatrix}$

2. Solution Steps

The notation $a_{ij}$ refers to the element in the $i$-th row and $j$-th column of the matrix $A$.

In this case, we are looking for $a_{12}$, which is the element in the first row and second column of the matrix $A$.

From the matrix $A = \begin{bmatrix} 1 & 0 & -2 \\ 3 & 2 & 1 \\ 4 & 0 & 3 \end{bmatrix}$, we can see that the element in the first row and second column is

0. Therefore, $a_{12} = 0$.

3. Final Answer

0