theorem Th32: :: MATRIX11:32

for n being Nat
for K being commutative Ring
for a, b being Element of K
for l being Nat
for pK, qK being FinSequence of K
for perm being Element of Permutations n st l in Seg n & len pK = n & len qK = n holds
for M being Matrix of n,K holds (Path_product (RLine (M,l,((a * pK) + (b * qK))))) . perm = (a * ((Path_product (RLine (M,l,pK))) . perm)) + (b * ((Path_product (RLine (M,l,qK))) . perm))