if A weren't singular and since elementary matrices aren't singular, multiplying the right hand from the left by you get a contradiction.
what does does this mean? are we not trying to prove that A is singular? there shouldnt be a contradction?
Read again and carefully: we supposed A is NON-SINGULAR, i.e. we supposed A is invertible, and we got a contradiction...and this is what you wanted, didn't you?
Read again and carefully: we supposed A is NON-SINGULAR, i.e. we supposed A is invertible, and we got a contradiction...and this is what you wanted, didn't you?
Tonio
oh ic, so we are trying to prove that A is not an elementaery matrix, right?
, and if A weren't singular and since elementary matrices aren't singular, multiplying the right hand from the left by you get a contradiction.
Tonio
, this line, isn't it Ek...E2E1A = B? does it make a different? And what does multiplying the right hand from the left mean, multiply that at the right side, or left side?
oh ic, so we are trying to prove that A is not an elementaery matrix, right?
No. We're trying to prove that A is singular. Of course, this includes A not being elementary since elem. matrices are non-singular, but our quest is way more general.
, this line, isn't it Ek...E2E1A = B? does it make a different? And what does multiplying the right hand from the left mean, multiply that at the right side, or left side?
I decided . but of course you can order the elem. matrices as you wish, and yes: multiplying from the left means at the left side, since matrix multiplication isn't commutative.
, and if A weren't singular and since elementary matrices aren't singular, multiplying the right hand from the left by you get a contradiction.
Tonio
ok, but why do I multiply [tex]A^{-1}E_K^{-1}...E_1^{-1}[/math? where is it from, is it the inverse of B? If I only multiply this on the left side, won't it change the equation?