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- scientia
- 2012-11-07 22:38:27
(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.
- princess snowwhite
- 2012-11-07 18:45:03
I HAVE TWO QUESTIONS-
1> If A be a non-zero column matrix and B be a non-zero row matrix, then
show that the rank of AB is 1.
2> If A and B be square matrices both of order n and of ranks p and q respectively, then
show that the rank of (AB) ≥ p + q - n.