To identify the matrix element [tex]\( a_{32} \)[/tex] from the given matrix [tex]\( A \)[/tex], let's follow these steps:
1. Understand matrix indexing: In a matrix, the element [tex]\( a_{ij} \)[/tex] refers to the element located in the [tex]\( i \)[/tex]-th row and [tex]\( j \)[/tex]-th column.
The matrix [tex]\( A \)[/tex] given is:
[tex]\[
A = \begin{pmatrix}
0 & -1 \\
1.5 & 3 \\
7 & -2
\end{pmatrix}
\][/tex]
2. Identify the element [tex]\( a_{32} \)[/tex]:
- The first index (3) indicates the row number, so we look at the 3rd row.
- The second index (2) indicates the column number, so we look at the 2nd column.
3. Find the third row of matrix [tex]\( A \)[/tex]:
[tex]\[
\begin{pmatrix}
7 & -2
\end{pmatrix}
\][/tex]
4. Locate the second element from the third row:
[tex]\[
-2
\][/tex]
Thus, the matrix element [tex]\( a_{32} \)[/tex] is [tex]\(-2\)[/tex].
So, the correct answer is [tex]\(\boxed{-2}\)[/tex].
