Extended frege and gaussian elimination

We show that the Gaussian Elimination algorithm can be proven correct with uniform Extended Frege proofs of polynomial size, and hence feasibly. More precisely, we give short uniform Extended Frege proofs of the tautologies that express the following: given a matrix A, the Gaussian Elimination algorithm reduces A to row-echelon form. We also show that the consequence of this is that a large class of matrix identities can be proven with short uniform Extended Frege proofs, and hence feasibly.