Definition add_row_mult_matrix { n : nat } (r1 r2 : ⟦ n ⟧%stn) (s : R) : Matrix R n n. Proof. intros i. induction (stn_eq_or_neq i r2). - refine ((@stdb_vector R _ i) +pw (@scalar_lmult_vec R s _ (@stdb_vector R _ r1))). - refine (@stdb_vector R _ i). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices.