© 2000−2019  P. BogackiSolving a system of linear equationsv. 1.25 

 PROBLEM

Solve the following system of 3 linear equations in 3 unknowns:

-3 x1 +1 x2-2 x3=-7 
5 x1 +3 x2-4 x3=2 
1 x1 +2 x2-3 x3=-1 

 SOLUTION

 Step 1: Transform the augmented matrix to the reduced row echelon form  (Show details)

 -3   1   -2    -7 
 5   3   -4   2 
 1   2   -3   -1 

can be transformed by a sequence of elementary row operations to the matrix

 1   0   1 
 7 		   0 
 0   1   -11 
 7 		  0 
 0   0   0   1 

 Step 2: Interpret the reduced row echelon form

The reduced row echelon form of the augmented matrix is

 1   0   1 
 7 		   0 
 0   1   -11 
 7 		  0 
 0   0   0   1 

which corresponds to the system

1 x1  +(1/7) x3=0
 1 x2 +(-11/7) x3=0
  0=1 

Equation 3 cannot be solved, therefore, the system has no solution (i.e. the system is inconsistent).

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