SOLUTION: [1 2 -1 | 5] [0 1 -2 | 1] [0 1 0 | 0] Answer(3-3z, 1+2z, z) and [1 2 1 | -3 ] [0 1 -3 | -1/2] [0 0 0 | 4 ] Answer(No Solutions) I know the answers but I would

Question 1131187: [1 2 -1 | 5]
[0 1 -2 | 1]
[0 1 0 | 0]
Answer(3-3z, 1+2z, z)
and
[1 2 1 | -3 ]
[0 1 -3 | -1/2]
[0 0 0 | 4 ]
Answer(No Solutions)
I know the answers but I would like to know how to get them as well.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

First write down the augmented matrix and begin Gauss-Jordan elimination:

Your matrix:

Find the pivot in the 1st column in the 1st row:

Find the pivot in the 2nd column in the 2nd row:

Eliminate the 2nd column:

Make the pivot in the 3rd column by dividing the 3rd row by 2:

Eliminate the 3rd column:

Solution set:

check your answer: Answer(,, )

(,, ) =(,, )

Your matrix:

Find the pivot in the 1st column in the 1st row:

Find the pivot in the 2nd column in the 2nd row:

Eliminate the 2nd column:

Solution set:
The system is inconsistent
The system of equations corresponding to this REF has as its third equation

This equation clearly has no solutions - no assignment of numerical values to , and will make the value of the expression equal to anything but zero. Hence the system has no solutions.

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