To identify the matrix element [tex]\( b_{11} \)[/tex] in matrix [tex]\( B \)[/tex], follow these steps:
1. First, observe the matrix [tex]\( B \)[/tex]:
[tex]\[
B = \left[ \begin{array}{lll}
6 & -3 & \frac{1}{2}
\end{array} \right]
\][/tex]
Here, [tex]\( B \)[/tex] is a 1x3 matrix (1 row and 3 columns).
2. In matrix notation, [tex]\( b_{ij} \)[/tex] refers to the element in the [tex]\( i \)[/tex]-th row and [tex]\( j \)[/tex]-th column. For [tex]\( b_{11} \)[/tex], it means the element in the first row and the first column.
3. Look at the element in the first row and the first column of matrix [tex]\( B \)[/tex]:
[tex]\[
B_{11} = 6
\][/tex]
Therefore, the matrix element [tex]\( b_{11} \)[/tex] is 6.
