| ■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 . . 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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