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(1) Suppose and . Then is an matrix. For , the th column of is and the th column of is . Hence any two columns of are linearly dependent. As is a nonzero matrix, it follows that its rank is 1. (2) This is harder to prove. It is called Sylvester's inequality: http://www.artofproblemsolving.com/Foru … hp?t=43691.
I HAVE TWO QUESTIONS 