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May 6th, 2017, 02:26 PM   #1
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Show matrix row equivalence

Greetings.
I'm trying to find a sequence of elementary row operations to show row equivalence of matrices \begin{pmatrix} 0 & 1 & 4 & 1 \\ 1 & 0 & 8 & 6 \\ \end{pmatrix} and \begin{pmatrix} -2 & 1 & -11 & -8 \\ -1 & 2 & 2 & 2 \\ \end{pmatrix} Unfortunately, the closest result I've come to is transforming the second matrix to \begin{pmatrix} 0 & 1 & 5 & 4 \\ 1 & 0 & 8 & 6 \\ \end{pmatrix} Can anyone help me find the right sequence or at least give a hint?
Thanks for your help.
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May 7th, 2017, 04:07 AM   #2
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Well think about it, you've already matched one of the two row vectors. So that means if the two matrices are equivalent then you'd have to show the remaining vectors (since there are two row vector) match in each matrix.
So do you think the first row vector from the first matrix
[0 1 4 1]
Can ever be transformed into
[0 1 5 4]?


Another way to ask this question is "Are these two vectors scaler multiples of each other?"
And in fact they aren't. The first two entries match but if you tried to scale the vectors so that the 3rd entries match, the second entries would stop matching.

So these matrices aren't equivalent
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May 7th, 2017, 05:11 AM   #3
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Quote:
Originally Posted by Gamegeck View Post
Well think about it, you've already matched one of the two row vectors. So that means if the two matrices are equivalent then you'd have to show the remaining vectors (since there are two row vector) match in each matrix.
So do you think the first row vector from the first matrix
[0 1 4 1]
Can ever be transformed into
[0 1 5 4]?


Another way to ask this question is "Are these two vectors scaler multiples of each other?"
And in fact they aren't. The first two entries match but if you tried to scale the vectors so that the 3rd entries match, the second entries would stop matching.

So these matrices aren't equivalent
I came to the same conclusion and asked my teacher this question, but she replied these matrices are row equivalent and there is a way to show that. She also mentioned the possibility of adding an extra column to these matrices, but I didn't understand what she meant.
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May 7th, 2017, 09:14 AM   #4
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Quote:
Originally Posted by ZsoSahaal View Post
I came to the same conclusion and asked my teacher this question, but she replied these matrices are row equivalent and there is a way to show that. She also mentioned the possibility of adding an extra column to these matrices, but I didn't understand what she meant.
you've got the two matrices in reduced row echelon form (one swap away from it anyway).

Two row equivalent matrices in reduced row echelon form will be equal.

Your two rre matrices are not equal and thus not row equivalent.

I'd press your teacher further on what she means.
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