Gaussian Elimination Example

-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:

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