Given the matrix $A$ listed below as a matrix over field $z\in \{0,1,2,3,4\}$, find the row reduced echelon form $B$ of $A$. List the elementary matrices used to reduce $A$ to $B$. $$A=\pmatrix{1 &2 &0 &3 \\ 2 &4 &1 &1 \\ 2 & 4 &0 &1 \\}$$

I am able to get the Matrix into the reduced row echelon form, the problem is that when I am getting my elementary matrices the way I reduce Matrix $A$ always makes it so my elementary matrices are not in the field. Please help me.

One way I tried was $$R_2 \leftarrow R_2-R_3$$ and $$R_3 \leftarrow 2R_1-R_3$$ that gets the matrix into reduced row echelon from but puts the elementary matrices outside of the field.



and we're done working over $\,\Bbb F_5:=\Bbb Z/5\Bbb Z\,$ . Can you now list the elementary matrices used, even if the first, and only, used operation is subdivided in two?

  • $\begingroup$ yes, i actually figured it out and did what you did. Thank you so much for helping me though. $\endgroup$
    – user547866
    Jan 15 '13 at 20:35

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.