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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.

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up vote 0 down vote accepted


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?

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

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