To find the element [tex]\( a_{12} \)[/tex] in a given matrix, we need to look at the element that is in the first row and second column.
Given the matrix:
[tex]\[
\begin{bmatrix}
2 & 4 & 4 & \frac{1}{2} \\
-3 & 0 & 3 & 4 \\
-6 & \frac{2}{3} & 3 & 4
\end{bmatrix}
\][/tex]
1. We first identify the first row of the matrix, which is:
[tex]\[ [2, 4, 4, \frac{1}{2}] \][/tex]
2. Next, we identify the second column of this row. The second column element in the first row is:
[tex]\[ 4 \][/tex]
Hence, the element [tex]\( a_{12} \)[/tex] in the given matrix is:
[tex]\[ 4 \][/tex]
Therefore, the correct answer is:
[tex]\[ 4 \][/tex]
