计算行列式|0-1-1-1||10-1-1||110-1||1110|

Question

计算行列式|0 -1 -1 -1||1 0 -1 -1||1 1 0 -1||1 1 1 0|

Answer 1

r4-r3,r3-r2
0 -1 -1 -1
1 0 -1 -1
0 1 1 0
0 0 1 1
r1+r3
0 0 0 -1
1 0 -1 -1
0 1 1 0
0 0 1 1
第1行依次与2,3,4行交换得(行列式变符号)
1 0 -1 -1
0 1 1 0
0 0 1 1
0 0 0 -1
行列式 = -1*(-1) = 1.