Reduced row echelon form: Difference between revisions

1 0 10 5▼

4 1 6 1▼

Create the first leading one by interchanging rows 1 and 2▼

1 0 01 5▼

3 1 −4 −1▼

4 1 6 1▼

Now subtract 3 times row 1 from row 2, and subtract 4 times row 1 from row 3. The result is▼

1 0 10 5▼

0 1 −34 −16▼

0 1 −34 −19▼

Now subtract row 2 from row 3 to obtain▼

1 0 10 5▼

0 1 −34 −16▼

0 0 0 −3▼

This means that the following reduced system of equations▼

x + 10z = 5▼

y − 34z = −16▼

0 +0 +0 = −3▼

is equivalent to the original system. In other words, the two have the same solutions. ▼

But this last system clearly has no solution (the last equation requires that x, y and z satisfy 0x+0y+0z = −3,▼

and no such numbers exist). ▼

Hence the original system has no solution.▼