title: Reduced Row Echelon Form (rref)
body: <p>I found that rref in Matlab does the gaussian elimination with patial pivoting Let A for example be a 5x9 matrix:</p>
  
  <pre><code>0.4898    0.2760    0.4984    0.7513    0.9593    0.8407    0.3500    0.3517    0.2858
  0.4456    0.6797    0.9597    0.2551    0.5472    0.2543    0.1966    0.8308    0.7572
  0.6463    0.6551    0.3404    0.5060    0.1386    0.8143    0.2511    0.5853    0.7537
  0.7094    0.1626    0.5853    0.6991    0.1493    0.2435    0.6160    0.5497    0.3804
  0.7547    0.1190    0.2238    0.8909    0.2575    0.9293    0.4733    0.9172    0.5678
  </code></pre>
  
  <p>rref(A) gives:</p>
  
  <pre><code>1.0000         0         0         0         0   10.9716   -6.2494   33.3062   16.0275
       0    1.0000         0         0         0   -2.2910    1.6003   -9.5889   -3.9001
       0         0    1.0000         0         0   -3.3952    1.8012   -6.8843   -3.4078
       0         0         0    1.0000         0   -8.3071    5.8617  -27.3981  -13.0805
       0         0         0         0    1.0000    4.2036   -2.4313   11.1545    5.2517
  </code></pre>
  
  <p>How to obtain the same result as rref by performing LU factorization of A? 
  I found that LU factorization does gauss elimination with partial pivoting as well. How to replace in a code rref with LU? 
  What are the steps to do after [L,U]=lu(A) to obtain the same result as rref(A) of the above example.</p>