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1. Show the the following pair is row equivalent
5 1 6
-1 0 1
2 2 2
0 1 3
and
4 -1 0
3 1 1
-1 1 -1
2 1 3
2. Show that the following pair is not row equivalent
2 1 3 4
1 -1 1 2
0 2 1 0
and
5 2 1 1
0 3 1 -1
2 -1 0 3
I know that if rank of two matrices are different they cannot be row equivalent, but in this question two ranks are the same (r=3)
Please help
have you tried putting both matrices in reduced row echelon form?
For Question1: The reduced forms are
5 1 6
0 1 11
0 0 -90
0 0 -8
and
4 -1 0
0 7/4 1
0 0 -10/7
0 0 15/7
but I dont see the correlation except 3rd and 4rd row are the same
Those are not in reduced row echelon form.
In reduced row echelon form, every row with nonzero entries should have a leading one. Leading ones should be the only nonzero entry in their respective columns.
A matrix "A" is row equivalent to "B" if elementary row operations applied to "A" can produce "B."
Two matrices are row equivalent if and only if they share the same reduced row echelon form.