Question

求教这个行列式怎么解?最好详细点,x 1 0 0 1 x 1 0 0 1 x 1 0 0 1 x

Answer 1

1-xr2

0 1-x^2 -x 0

1 x 1 0

0 1 x 1

0 0 1 x

r1-(1-x^2)r3

0 0 x^3-2x x^2-1

1 x 1 0

0 1 x 1

0 0 1 x

r1-(x^3-2x)r4

0 0 0 -x^4+3x^2-1

1 x 1 0

0 1 x 1

0 0 1 x

= (-1)^(1+4)(-x^4+3x^2-1)

= x^4-3x^2+1