Question: pls the method used to reduce the matrix A into the REF is a bit clumsy to me. pls explain to me and help me

pls the method used to reduce the matrix A into the REF is a bit clumsy to me. pls explain to me and help me understand. Thank you.
Examples 1 Find a basis for the linear code c=457 for S={11101, 10110 01011 11010} Solution. Fillol 111 li lol oroll olol OO!! 1010 oo!!! 1 10llo 01011 010 11010 ooo {111, Holly outl} is a basis for c = 22 Another REF 7 A is rilo olloo ooli a {mod, 6100, coll} is also a basis for a
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