高等数学物理类专业用线性代数标准答案 2 0 -4

Question

-1
3 6 1 1
3 -13 12 -1
2 3 3 1
用行列式的性质计算

Answer 1

r2+r1,r3-r1,r4+r1
2 0 -4 -1
5 6 -3 0
1 -13 16 0
4 3 -1 0

r2-3r4,r3+16r4
2 0 -4 -1
-7 -3 0 0
65 35 0 0
4 3 -1 0

r3+12r2
2 0 -4 -1
-7 -3 0 0
-19 -1 0 0
4 3 -1 0

r2-3r3
2 0 -4 -1
50 0 0 0
-19 -1 0 0
4 3 -1 0

= (-1)^t(4123) *(-1)*50*(-1)*(-1)
= 50.