Helper

rouche1

Section RoucheCapelliTheorems

Type Lemma

Proof Lines 8

Lemma rouche1 m n (A : 'M[R]_(m,n)) (B : 'rV_n) : (exists x, x *m A = B) <-> (\rank A = \rank (col_mx A B)).

Rouché-Capelli Theorem (Part 1): System xA = B has a solution iff rank(A) = rank([A; B]). The augmented matrix has same rank as coefficient matrix.

This lemma does not use any other lemmas from the stats.

No lemmas in the stats use this lemma.

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