线性代数排列式 求解~~
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线性代数排列式 求解~~
线性代数排列式 求解~~
线性代数排列式 求解~~
x a ...a
a x ...a
.
a a ...x
=[x+(n-1)a]
1 a ...a
1 x ...a
.
1 a ...x
=[x+(n-1)a]
1 a ...a
0 x-a ...0
.
0 0 ...x-a
=[x+(n-1)a](x-a)^(n-1)
x -1 0 ...0 0
0 x -1 ...0 0
.
0 0 0 ...x -1
an an-1 an-2 ...a2 x+a1
=
x -1 0 ...0 0
x^2 0 -1 ...0 0
.
x^(n-1) 0 0 ...0 -1
(x^n)an an-1 an-2 ...a2 a1
=
x -1 0 ...0 0
x^2 0 -1 ...0 0
.
x^(n-1) 0 0 ...0 -1
(x^n)an+x^(n-1)a1+...+xan-1 0 0 ...0 0
=(x^n)an+x^(n-1)a1+...+xan-1