计算行列式| xaaaaxaaaaxaaaax |.

问题描述:

计算行列式

x a a a
a x a a
a a x a
a a a x
 |.

行列式

.
x a a a
a x a a
a a x a
a a a x
.
=
.
x a a a
a−x x−a 0 0
a−x 0 x−a 0
a−x 0 0 x−a
.
=
.
x+3a a a a
0 x−a 0 0
0 0 x−a 0
0 0 0 x−a
.
=(x+3a)(x-a)3