Question

线性代数基础，要求化为下三角行列式求该四阶行列式

要求化为下三角行列式，老师的要求，要凑零，谢谢！

Answer 1

行列式D=
3 1 -1 2
-5 1 3 -4
2 0 1 -1
1 -5 3 -3 c4+c3，c1-2c3
=
5 1 -1 1
-11 1 3 -1
0 0 1 0
-5 -5 3 0 r2+r1，r4-3r3
=
5 1 -1 1
-6 2 2 0
0 0 1 0
-5 -5 0 0 r3-1/2r2
=
5 1 -1 1
-6 2 2 0
3 -1 0 0
-5 -5 0 0 c2-c1
=
5 -4 -1 1
-6 8 2 0
3 -4 0 0
-5 0 0 0
于是D= -5*(-4)*2*1=40

Answer 2

Answer 3

过程