Would someone please show me how to show that:
Thank you.
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Would someone please show me how to show that:
Thank you.
Define A, B and C.Quote:
Originally Posted by itpro
Would someone please show me how to show that:
Thank you.
They areQuote:
Originally Posted by alexmahone
matrices.
They can't just be any n x n matrices, can they? What is the relationship among them?Quote:
Originally Posted by itproThey are
Sorry, missed that:Quote:
Originally Posted by alexmahone
My intuition for the proof is that rank(A) and rank(b) is at most n and since addition preserves the dimension they will be at most of the rank of a C
as C rank is less or equal to n.
what you want to show is that:
rank(A) + rank(B) ≤ rank(A+B).
but this is not true. suppose that A =
[1 0]
[0 0] and that B =
[-1 0]
[ 0 0].
clearly, A and B both have rank 1, so rank(A) + rank(B) = 1 + 1 = 2.
however, A+B is the 0-matrix, which has rank 0, and 2 is not less than or equal to 0.