
Linear Algebra Linear Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: CA Posts: 1,206 Thanks: 614  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.  

Tags 
equivalence, matrices, matrix, row, rowequivalnce, show 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Show that the Google Matrix is stochastic  tawirma98  Linear Algebra  1  October 5th, 2016 04:59 PM 
Show that there exists a matrix with certain entries and det  annakar  Linear Algebra  0  January 10th, 2013 10:58 AM 
Show this Logical Equivalence  Jack Spicer  Applied Math  8  February 3rd, 2012 06:23 AM 
Proof for matrix equivalence  mathHuji  Linear Algebra  0  February 6th, 2011 05:32 AM 
Show equivalence of definitions  brunojo  Linear Algebra  2  May 28th, 2009 03:04 PM 