EQUALITY OF ROW AND COLUMN RANK (o'Neil's proof) Is there smt wrong? http://www.mediafire.com/imageview.php?quickkey=znorkrmk3k1otjd&thumb=6 Theorem 7.9: EQUALITY OF ROW AND COLUMN RANK Proof: Page 210. It writes:.... so the dimension of this column space is AT MOST r (equal to r if these columns are linearly independent, less than r if they are not) I THINK THIS IS WRONG. Look at the r vectors: 1 0 0 1 : 0 0 : BETAr+1,1 BETAr+1,2 : BETAm1 BETAm2 The first r columns of these r vectors are e1,e2,...er. Hence, they are DEFINITELY LINEARLY INDEPENDENT. There is no way to obtain 1 in the first coordinate of the first of the r vectors from the remaining r-1 vectors since the 1st coordinate of all of the remaining r-1 vectors are all 0. Hence, the correct one should be: so the dimension of this column space is EXACTLY r. Where am I wrong? or O'neil's is really wrong as I indicated.