设四阶行列式D的第一行元素为a11=1 a12=3 a13=8 a14=-5第一行元素的余之式为M11=7 M12=0 M13=6 M14=9，求D

Question

如题所述

Answer 1

注意到 Aij = (-1)^(i+j) Mij
由行列式展开定理得
D = a11A11+a12A12+a13A13+a14A14
= a11M11-a12M12+a13M13-a14M14
= 1*7 - 3*0 + 8*6 - (-5)*9
= 100.