Let E Be An N X N Elementary Matrix And A Be An N X N Matrix Which Of The Follow

Let E be an n x n elementary matrix and A be an n x  n matrix. Which of the following

statements are ALWAYS true? (RS=row space, NS=Nullspace, CS=column space)

(i) NS(EA) = NS(E)

(ii) RS(EA) = RS(A)

(iii) CS(EA) = CS(A)

(iv) RS(EAT ) = CS(A)

(v) NS(A) = NS(AE)

A. (ii) and (iii)

B. (i) and (ii)

C. (ii) and (iv)

D. (i), (ii) and (v)

E. None of the above

 

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