行列式的展开,降阶法求0abaaobaba0aabao四阶行列式0abaaoabba0aaba0

Question

行列式的展开,降阶法求 0 a b a a o b a b a 0 a a b a o
四阶行列式
0 a b a
a o a b
b a 0 a
a b a 0

Answer 1

r3-r1,r4-r2 先化简一下
0 a b a
a 0 a b
b 0 -b 0
0 b 0 -b
按第1列展开降阶
= -a*
a b a
0 -b 0
b 0 -b
+ b*
a b a
0 a b
b 0 -b
= -2a^2b^2 + b(b^3 - 2a^2b)
= b^4-4a^2b^2.