 | ■No25880に返信(社会人10年さんの記事)
> 次の連立一次方程式を解け（a,bは定数）なんですが、
>
> ax[1]+x[2]+x[3]+・・・+x[n]=b
> x[1]+ax[2]+x[3]+・・・+x[n]=b
>
> ・・・・・・
>
> x[1]+x[2]+x[3]+・・・+ax[n]=b
In[2]:=
Inverse[{{a, 1}, {1, a}}];
MatrixForm[%]
Out[3]//MatrixForm=
MatrixForm[{{a/(-1 + a^2),
-(1/(-1 + a^2))}, {-(1/(-1 + a^2)),
a/(-1 + a^2)}}]
In[4]:=
{{a, 1}, {1, a}} . {x[1], x[2]}
Out[4]=
{a*x[1] + x[2], x[1] + a*x[2]}
In[5]:=
Solve[% == {b, b}, {x[1], x[2]}]
Out[5]=
{{x[1] -> b/(1 + a), x[2] -> b/(1 + a)}}<----◎２
In[6]:=
Inverse[{{a, 1, 1}, {1, a, 1}, {1, 1, a}}];
MatrixForm[%]
Out[7]//MatrixForm=
MatrixForm[{{(-1 + a^2)/(2 - 3*a + a^3),
(1 - a)/(2 - 3*a + a^3),
(1 - a)/(2 - 3*a + a^3)},
{(1 - a)/(2 - 3*a + a^3),
(-1 + a^2)/(2 - 3*a + a^3),
(1 - a)/(2 - 3*a + a^3)},
{(1 - a)/(2 - 3*a + a^3),
(1 - a)/(2 - 3*a + a^3),
(-1 + a^2)/(2 - 3*a + a^3)}}]
In[8]:=
{{a, 1, 1}, {1, a, 1}, {1, 1, a}} .
{x[1], x[2], x[3]}
Out[8]=
{a*x[1] + x[2] + x[3], x[1] + a*x[2] +
x[3], x[1] + x[2] + a*x[3]}
In[9]:=
Solve[% == {b, b, b}, {x[1], x[2], x[3]}]
Out[9]=
{{x[1] -> b/(2 + a), x[2] -> b/(2 + a),
x[3] -> b/(2 + a)}}<-----------------◎３
In[10]:=
Inverse[{{a, 1, 1, 1}, {1, a, 1, 1},
{1, 1, a, 1}, {1, 1, 1, a}}];
MatrixForm[%]
Out[11]//MatrixForm=
MatrixForm[{{(2 - 3*a + a^3)/
(-3 + 8*a - 6*a^2 + a^4),
(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4), (-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4),
(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4)}, {(-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4),
(2 - 3*a + a^3)/(-3 + 8*a - 6*a^2 +
a^4), (-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4),
(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4)}, {(-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4),
(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4), (2 - 3*a + a^3)/(-3 + 8*a -
6*a^2 + a^4), (-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4)},
{(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4), (-1 + 2*a - a^2)/
(-3 + 8*a - 6*a^2 + a^4),
(-1 + 2*a - a^2)/(-3 + 8*a - 6*a^2 +
a^4), (2 - 3*a + a^3)/(-3 + 8*a -
6*a^2 + a^4)}}]
In[12]:=
{{a, 1, 1, 1}, {1, a, 1, 1}, {1, 1, a, 1},
{1, 1, 1, a}} . {x[1], x[2], x[3], x[4]}
Out[12]=
{a*x[1] + x[2] + x[3] + x[4],
x[1] + a*x[2] + x[3] + x[4],
x[1] + x[2] + a*x[3] + x[4],
x[1] + x[2] + x[3] + a*x[4]}
In[13]:=
Solve[% == {b, b, b, b}, {x[1], x[2], x[3],
x[4]}]
Out[13]=
{{x[1] -> b/(3 + a), x[2] -> b/(3 + a),
x[3] -> b/(3 + a), x[4] -> b/(3 + a)}}<-----◎４
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と 帰納的に し、 誰でも 予想叶う ；
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿<----◎ｎ
http://www.youtube.com/watch?v=drv6_LcWSkQ
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿<----◎ｎ+1
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