Let A be an m x n matrix of rank r (a) Suppose C (A B) is an m Atilde k matrix, k n, whose first n columns are the same as the columns of A Prove that rank C yen rank A Give an example with rank C rank A with rankC rank A (b) Let Be a j Atilde n matrix, j m, whose first m rows are the same as those...

a Under elementary row operations the reduced form of C wil ...

Let A be an m x n matrix of rank r. (a) Suppose C = (A B)

Question:

Let A be an m x n matrix of rank r.
(a) Suppose C = (A B) is an m Ã— k matrix, k > n, whose first n columns are the same as the columns of A. Prove that rank C ‰¥ rank A. Give an example with rank C = rank A; with rankC > rank A.
(b) Let

Be a j Ã— n matrix, j > m, whose first m rows are the same as those of A. Prove that rank E ‰¥ rank A. Give an example with rank E = rank A; with rank E > rank A.