4. Solve the system of equations. 


Augmented matrix for given system of equations
solution using GaussJordan elimination
Your matrix
X1  X2  X3  b  

1  2  1  1  7 
2  1  3  4  19 
3  1  4  3  18 
Find the pivot in the 1st column and swap the 2nd and the 1st rows
X1  X2  X3  b  

1  1  3  4  19 
2  2  1  1  7 
3  1  4  3  18 
Eliminate the 1st column
X1  X2  X3  b  

1  1  3  4  19 
2  0  5  7  31 
3  0  1  1  1 
Find the pivot in the 2nd column and swap the 3rd and the 2nd rows
X1  X2  X3  b  

1  1  3  4  19 
2  0  1  1  1 
3  0  5  7  31 
Eliminate the 2nd column
X1  X2  X3  b  

1  1  0  7  22 
2  0  1  1  1 
3  0  0  12  36 
Make the pivot in the 3rd column by dividing the 3rd row by 12
X1  X2  X3  b  

1  1  0  7  22 
2  0  1  1  1 
3  0  0  1  3 
Eliminate the 3rd column
X1  X2  X3  b  

1  1  0  0  1 
2  0  1  0  2 
3  0  0  1  3 
Solution set:
x = 1
y = 2
z = 3
C. There is one solution (–1, 2, –3).
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