-mariacs

Take the following matrix and change it to Echelon form:

4 8 14 20 R1

6 -8 10 16 R2

12 20 -4 2 R3

The first step is to multiply R1 by 1/4:

1 2 3.5 5

6 -8 10 16

12 20 -4 2

Next is to multiply R1 by -6 and add it to R2:

1 2 3.5 5

0 -20 -11 -14

12 -20 -4 2

Then you'd multiply R1 by -12 and add it to R3:

1 2 3.5 5

0 -20 -11 -14

0 -4 -46 -58

Next is to multiply R2 by -1/20:

1 2 3.5 5

0 1 .55 .7

0 -4 -46 -58

Then you'd multiply R2 by 4 and add it to R3:

1 2 3.5 5

0 1 .55 .7

0 0 -43.8 -55.2

Next would be to multiply R3 by -1/43.8:

1 2 3.5 5

0 1 .55 .7

0 0 1 1.26027

Then if you want to get the reduced row echelon form,

you'd multiply R2 by -2 and add it to R1:

1 0 2.4 3.6

0 1 .55 .7

0 0 1 1.26027

Next would be to multiply R3 by -2.4 and add it to R1:

1 0 0 .57534

0 1 .55 .7

0 0 1 1.26027

Then you'd multiply R3 by -.55 and add it to R2:

1 0 0 .57534

0 1 0 .00685

0 0 1 1.26027

I'd recommend just plugging in the problem into Octave/MatLab c: