Answer :
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]
[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]