Question

求这两道行列式的做法！！！

Answer 1

1. D1 = 2*
|a11 a13 a11-2a12|
|a21 a23 a21-2a22|
|a31 a33 a31-2a32|
D1 = 2*
|a11 a13 -2a12|
|a21 a23 -2a22|
|a31 a33 -2a32|
D1 = -4*
|a11 a13 a12|
|a21 a23 a22|
|a31 a33 a32|
D1 = 4D = 2
2. x1+x2+x3 = -p
x1x2+x1x3+x2x3 = q
x1x2x3 = 0
D =
|x1 x2 x3|
|x3 x1 x2|
|x2 x3 x1|
D =
|x1+x2+x3 x2 x3|
|x1+x2+x3 x1 x2|
|x1+x2+x3 x3 x1|
D =
|-p x2 x3|
| 0 x1-x2 x2-x3|
|0 x3-x2 x1-x3|
D = -p[(x1)^2-x1x2-x1x3+x2x3 +(x2)^2-2x2x3+(x3)^2]
= -p[(x1)^2+(x2)^2+(x3)^2-x1x2-x1x3-x2x3]
=-p[(x1+x2+x3)^2-3(x1x2+x2x3+x3x1)]
= -p(p^2-3q) = p(3q-p^2)