Talk:Reduced row echelon form: Difference between revisions

The algorithm has a Bug.

It does NOT do the SWAP. No conditions are checked

It does NOT work for this example matric

Solve the following system of equations.

3x+y− 4z=−1

x +10z= 5

4x+y+ 6z= 1

Solution. The corresponding augmented matrix is

3 1 −4 −1

1 0 10 5

4 1 6 1

Create the first leading one by interchanging rows 1 and 2

1 0 10 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= −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.