Row reduced echelon form

renjer · 2006-06-13 22:10:59

Reducing matrices to row echelon form is easy, however, most of the time I seem to go around in circles.

Take this matrix for example:

1 1 1
1 2 -2
1 -2 2

What is the easiest way to go, and how do you know what to do?

Zhylliolom · 2006-06-13 22:35:08

To reduce to echelon form, apply Gaussian elimination. To do this you take m = -a[sub]i1[/sub]/a[sub]11[/sub] times the i[sup]th[/sup] row and add the 1st row to it. This will sound a lot better when you see the example worked out:

is our matrix. Let row 1 = L[sub]1[/sub], row 2 = L[sub]2[/sub], and row 3 = L[sub]3[/sub].

For row 2, m = -1. So replace row 2 with -L[sub]1[/sub] + L[sub]2[/sub] and get

For row 3, m = -1. So replace row 3 with -L[sub]1[/sub] + L[sub]3[/sub] and get

Now we must apply the algorithm again, using a[sub]22[/sub] = 1 as a pivot.

m = 3 this time (-3/-1), so replace row 3 with -L[sub]2[/sub] + L[sub]3[/sub] and get

At this point, the matrix is in echelon form, which is what I believe you asked for. If you happened to mean row canonical form, I'll make a post for that. Please ask any questions, as I am unsure how clearly I explained this algorithm for you.

krassi_holmz · 2006-06-13 22:49:03

Starting up, in every row eliminate one more element.

krassi_holmz · 2006-06-13 22:53:08

I'm new to this, but I have a feeling that every matrixes can be reduced.
And this is useful for calculationg the determinant:it is equal to the porduct of the diagonal elements:
for the example, det A=1.1.-8=-8.

krassi_holmz · 2006-06-13 22:54:18

And the gaussian reduction can be use not only with square matrixes.

renjer · 2006-06-14 00:16:35

Oh, actually I was wanting an easy way to get to reduced row echelon form, not just the normal echelon form. It's just sometimes driving me crazy. It's always like I've reduced an element in the matrix to zero, but because of another row operation, the zero becomes a number again, and I'll be going around in circles.

And this row reduction to reduced row echelon form, is for me to find eigenvectors.

Math Is Fun Forum

#1 2006-06-13 22:10:59

Row reduced echelon form

#2 2006-06-13 22:35:08

Re: Row reduced echelon form

#3 2006-06-13 22:49:03

Re: Row reduced echelon form

#4 2006-06-13 22:53:08

Re: Row reduced echelon form

#5 2006-06-13 22:54:18

Re: Row reduced echelon form

#6 2006-06-14 00:16:35

Re: Row reduced echelon form

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