0
$\begingroup$

Can anyone explain this conceptual problem?

If an $n \times n$ matrix is in row reduced echelon form, explain why it is either the identity matrix or else has a row of zeroes?

Thanks

$\endgroup$
  • $\begingroup$ The choice of a good answer here depends a lot on what you already know; there are a lot of options, but some require prior knowledge that you might not have. Do you already know that a linear system $Ax=b$ has either 0,1, or infinitely many solutions? Each of these cases can be "read off" from the echelon form (or reduced echelon form) of the augmented matrix for the system. $\endgroup$ – Ian May 17 '15 at 19:52
  • $\begingroup$ Do you have an example of a matrix that is in reduced row echelon form but isn't the identity matrix? Why can't you get it in the form of the identity matrix? $\endgroup$ – Maths student May 17 '15 at 19:52
1
$\begingroup$

If it doesn't have row of zeros then all the rows will have a leading 1.Which will make it a identity matrix.

$\endgroup$
  • $\begingroup$ @pasie15 The rule is for RREF (row reduced echelon matrix) not REF (reduced echelon matrix) $\endgroup$ – Shubham Ugare May 17 '15 at 19:54
  • $\begingroup$ In the texts I've seen (Lay and Strang), the form given by "rref" is called "reduced echelon form", not "row reduced echelon form". $\endgroup$ – Ian May 17 '15 at 19:55
  • $\begingroup$ A matrix is in reduced row echelon form (also called row canonical form) if it satisfies the following conditions: It is in row echelon form. Every leading coefficient is 1 and is the only nonzero entry in its column.(wiki) $\endgroup$ – Shubham Ugare May 17 '15 at 19:55
  • $\begingroup$ okay..It was different in the book i read..but the answer is according to ref itself.. $\endgroup$ – Shubham Ugare May 17 '15 at 19:56

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.