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Transcript
Vector spaces - matrix row-eschelon form Lemma If M is any matrix, then M can by applying elementary operations 1,2,3,4 it can be transformed into a matrix Mï¢ in row echelon form. Proof (sketch) Proceed iteratively in steps 1...k as follows: Step i ⢠Perform row permutation (if such exists) that places in i-th position row with a non-zero element in i-th column. Let it be row v. If there are no appropriate permutation, perform first column permutation that places non-zero column in i-th position. ⢠Add to each of other rows vector av, where a is chosen such that after the addition the row has value 0 in i-th position.
