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May 6th, 2017, 02:26 PM  #1 
Newbie Joined: May 2017 From: Prague Posts: 2 Thanks: 0  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. 
May 7th, 2017, 04:07 AM  #2 
Newbie Joined: Nov 2013 Posts: 29 Thanks: 1 
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 
May 7th, 2017, 05:11 AM  #3  
Newbie Joined: May 2017 From: Prague Posts: 2 Thanks: 0  Quote:
 
May 7th, 2017, 09:14 AM  #4  
Senior Member Joined: Sep 2015 From: USA Posts: 2,549 Thanks: 1399  Quote:
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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equivalence, matrices, matrix, row, rowequivalnce, show 
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