Certainly! Let's go through the process of identifying the values for the elements in the given augmented matrix [tex]\( A \)[/tex]. The matrix [tex]\( A \)[/tex] is defined as:
[tex]\[
A = \left[\begin{array}{lll}
a_{11} & a_{12} & a_{13} \\
a_{21} & a_{22} & a_{23}
\end{array}\right]
\][/tex]
We need to determine the values of the elements [tex]\( a_{11}, a_{12}, a_{13}, a_{21}, a_{22}, \)[/tex] and [tex]\( a_{23} \)[/tex].
Given the results, these values are:
- [tex]\( a_{11} = 1 \)[/tex]
- [tex]\( a_{12} = 2 \)[/tex]
- [tex]\( a_{13} = 3 \)[/tex]
- [tex]\( a_{21} = 4 \)[/tex]
- [tex]\( a_{22} = 5 \)[/tex]
- [tex]\( a_{23} = 6 \)[/tex]
Thus, the detailed assignment of the values for each element in the matrix [tex]\( A \)[/tex] is as follows:
- The element in the first row and first column, [tex]\( a_{11} \)[/tex], has a value of 1.
- The element in the first row and second column, [tex]\( a_{12} \)[/tex], has a value of 2.
- The element in the first row and third column, [tex]\( a_{13} \)[/tex], has a value of 3.
- The element in the second row and first column, [tex]\( a_{21} \)[/tex], has a value of 4.
- The element in the second row and second column, [tex]\( a_{22} \)[/tex], has a value of 5.
- The element in the second row and third column, [tex]\( a_{23} \)[/tex], has a value of 6.
So, we have:
[tex]\[
\begin{aligned}
a_{11} &= 1 \\
a_{12} &= 2 \\
a_{13} &= 3 \\
a_{21} &= 4 \\
a_{22} &= 5 \\
a_{23} &= 6 \\
\end{aligned}
\][/tex]
Therefore, the final augmented matrix [tex]\( A \)[/tex] with the identified values is:
[tex]\[
A = \left[\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6
\end{array}\right]
\][/tex]
