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Sagot :
Let's match each system of equations to its solution represented by an augmented matrix step-by-step.
### System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]
### System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
### Summary
1. System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]
2. System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
3. System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
4. System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
### System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]
### System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
### System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]
Corresponding Solution as an Augmented Matrix:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
### Summary
1. System of Equations 1:
[tex]\[ \begin{aligned} x + y + z & = 1100 \\ x - 2y - z & = -500 \\ 2x + 3y + 2z & = 2600 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 750 \\ 0 & 1 & 0 & 850 \\ 0 & 0 & 1 & 1000 \end{array}\right] \][/tex]
2. System of Equations 2:
[tex]\[ \begin{aligned} x + y + z & = 2600 \\ x + y - z & = 600 \\ 2x + y + 2z & = 4350 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 400 \\ 0 & 1 & 0 & 600 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
3. System of Equations 3:
[tex]\[ \begin{aligned} x + y + z & = 1900 \\ x - y - 2z & = -2000 \\ 2x + 2y + z & = 2900 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 1300 \\ 0 & 1 & 0 & 1100 \\ 0 & 0 & 1 & 900 \end{array}\right] \][/tex]
4. System of Equations 4:
[tex]\[ \begin{aligned} x + y + z & = 3300 \\ x + y - z & = 1500 \\ 2x + 3y + 2z & = 7700 \\ \end{aligned} \][/tex]
Solution:
[tex]\[ \left[\begin{array}{ccc|c} 1 & 0 & 0 & 500 \\ 0 & 1 & 0 & 400 \\ 0 & 0 & 1 & 200 \end{array}\right] \][/tex]
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