Suppose that all of the diagonal entries of an upper triangular ma- trix Re M,, (R)...

 

Transcribed Image Text:

Suppose that all of the diagonal entries of an upper triangular ma- trix Re M,, (R) are all nonzero. Prove that R is a product of "(+1) elementary matrices. [3] 2 Let A € Mxm (R) and BE Mmxn(R) and suppose that AB = In Does this imply that BA= Im? Give an example or proof. [2] Suppose that all of the diagonal entries of an upper triangular ma- trix Re M,, (R) are all nonzero. Prove that R is a product of "(+1) elementary matrices. [3] 2 Let A € Mxm (R) and BE Mmxn(R) and suppose that AB = In Does this imply that BA= Im? Give an example or proof. [2]