线性代数行列式计算a b 0 0 0..0 00 a b 0 0 ..0 00 0 a b...0 0 0.0 0 0 .0 a_数学解答

线性代数行列式计算
a b 0 0 0..0 0
0 a b 0 0 ..0 0
0 0 a b...0 0 0
.
0 0 0 .0 a b
b 0 0 .0 0 a

人气：415 ℃　时间：2019-10-18 17:13:14

解答

按照第一列展开
原式=a×
ab000.0
0a000.0
.
00000.a
+b×(-1)的n+1次方×
b000.0
ab00.0
0ab0.0
.
0000000000ab
=a的n次方+（-1）的n次方×b的n次方我写漏啊上面是n+1次方啊即按照第一列展开原式=a×ab000.....00a000.....0...........00000.....a+b×(-1)的n+1次方×b000.......0ab00.......00ab0.......0.............00000....ab=a的n次方+（-1）的n+1次方×b的n次方