Sure, let's identify the matrix element [tex]\( a_{31} \)[/tex] in the given matrix [tex]\( A \)[/tex]:
[tex]\[
A = \begin{pmatrix}
0 & -1 \\
1.5 & 3 \\
7 & -2
\end{pmatrix}
\][/tex]
The subscript [tex]\( a_{ij} \)[/tex] represents the element located at the [tex]\( i \)[/tex]-th row and [tex]\( j \)[/tex]-th column of the matrix.
Here, [tex]\( a_{31} \)[/tex]:
- The first index (3) indicates the row.
- The second index (1) indicates the column.
So, [tex]\( a_{31} \)[/tex] is the element in the 3rd row and 1st column of the matrix [tex]\( A \)[/tex].
Let's examine the 3rd row:
[tex]\[
\begin{pmatrix}
7 & -2
\end{pmatrix}
\][/tex]
Now we look at the 1st element in this row:
[tex]\[
7
\][/tex]
Therefore, the matrix element [tex]\( a_{31} \)[/tex] is [tex]\( 7 \)[/tex].
