To identify the matrix element [tex]\( a_{12} \)[/tex] in the matrix [tex]\( A \)[/tex], we should understand the notation used for matrix elements. The subscript [tex]\( a_{ij} \)[/tex] refers to the element located in the [tex]\( i \)[/tex]-th row and [tex]\( j \)[/tex]-th column of the matrix.
Given the matrix [tex]\( A \)[/tex]:
[tex]\[
A = \begin{pmatrix}
0 & -1 \\
1.5 & 3 \\
7 & -2
\end{pmatrix}
\][/tex]
We need to locate the element [tex]\( a_{12} \)[/tex]:
- The first subscript [tex]\( 1 \)[/tex] specifies the row number.
- The second subscript [tex]\( 2 \)[/tex] specifies the column number.
So, [tex]\( a_{12} \)[/tex] is found at the intersection of the first row and the second column.
Looking directly at the matrix [tex]\( A \)[/tex]:
[tex]\[
A = \begin{pmatrix}
0 & -1 \\
1.5 & 3 \\
7 & -2
\end{pmatrix}
\][/tex]
From the above matrix:
- The first row is [tex]\( \left( 0, -1 \right) \)[/tex]
- In this row, the element in the second column is [tex]\( -1 \)[/tex]
Therefore, [tex]\( a_{12} = -1 \)[/tex].
Thus, the correct answer is:
[tex]\[
-1
\][/tex]
