Question

本人数学小白，求下面线性代数行列式解法。

求详细解答~~谢谢~~

Answer 1

(1)解: 当n=1时, D1=a1-b1
当n=2时, D2=
a1-b1 a1-b2
a2-b1 a2-b2
= (a1-b1)(a2-b2) - (a1-b2)(a2-b1).

当n>=3时
r2-r1,r3-r1
则第2,3行分别为
a2-a1 a2-a1 ... a2-a1
a3-a1 a3-a1 ... a3-a1
两行成比例, 行列式等于0

(2)解:
Dn =
ri-r2, i=1,3,4,...,n 所有行减第2行
-1 0 0 ... 0
2 2 2 ... 2
0 0 1 ... 0
... ...
0 0 0 ... n-2

= -2(n-2)!

Answer 2

原式=a1-b1 a1-b2 ........a1-bn
a2-a1 a2-a1 .........a2-a1
..........................................
an-a1 an-a1 .......an-a1
=a1-b1 a1-b2 ......... a1-a1
0 0 ..........a2-a1
.................................................
0 0 ..............an-a1
= 0
x写了这么多，给个最佳吧！