[Math] Reduced row echelon form without introducing fractions at any intermediate stage

linear algebramatrices

How can I reduce this matrix to reduced row echelon form but without using fractions in intermediary steps (I can use them in elementary row operations just not in the results in the matrix)

$$
\begin{pmatrix}
2 & 1 & 3 \\
0 & -2 & 7 \\
3 & 4 & 5 \\
\end{pmatrix}
$$

I been trying for several hours and can seem to figure that out.
Is it even possible?

Thanks for any help

Best Answer

Yes, it is possible. Furthermore, there does exist some algorithms to do this, such as the fraction-free Gaussian elimination, see, e.g., E H Bareiss. Sylvester's identity and multistep integer-preserving Gaussian elimination. Math. Comput., 22(103):565-578, 1968.

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