To identify the matrix element [tex]\( b_{12} \)[/tex] in the given matrix [tex]\( B \)[/tex], follow these steps:
1. Understand the Matrix Layout:
Matrix [tex]\( B \)[/tex] is given as:
[tex]\[
B = \left[\begin{array}{lll}
6 & -3 & \frac{1}{2}
\end{array}\right]
\][/tex]
This is a 1-row by 3-column matrix, meaning it has one row and three columns.
2. Identify Row and Column Indices:
The element [tex]\( b_{ij} \)[/tex] refers to the element in the [tex]\( i \)[/tex]-th row and [tex]\( j \)[/tex]-th column of the matrix. Here, [tex]\( b_{12} \)[/tex] refers to the element in the 1st row and 2nd column.
3. Locate [tex]\( b_{12} \)[/tex]:
- The 1st row is the only row available: [tex]\([6, -3, \frac{1}{2}]\)[/tex].
- The 2nd column in this row contains the element [tex]\(-3\)[/tex].
Thus, the matrix element [tex]\( b_{12} \)[/tex] is [tex]\(-3\)[/tex].
