行列式[3-2-54,-528-5,-247-3,2-3-58]求该行列式.

Question

行列式[3 -2 -5 4,-5 2 8 -5 ,-2 4 7 -3,2 -3 -5 8]
求该行列式.

Answer 1

r2+r1,r3+2r1,r4-r1
3 -2 -5 4
-2 0 3 -1
4 0 -3 5
-1 -1 0 4
r1-2r4
5 0 -5 -4
-2 0 3 -1
4 0 -3 5
-1 -1 0 4
按第2列展开 D=-1*
5 -5 -4
-2 3 -1
4 -3 5
r3+r2
5 -5 -4
-2 3 -1
2 0 4
c3-2c1
5 -5 -14
-2 3 3
2 0 0
c3-c2
5 -5 -9
-2 3 0
2 0 0
= - 2*3*9 = -54