余因子展開法 |
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[演習] [0,0,1] [0,2,0] の逆行列を求めよ。 [3,0,0] |
wxMaxima利用 |
行列式の計算 | 0,0,1 | | 0,2,0 |=-6 | 3,0,0 | 余因子 a11= 0,a12=0, a13=-6 a21= 0,a22=-3,a23=0 a31=-2,a32=0, a33=0 余因子行列 [0, 0, 1] [0,1/2,0] [1/3,0,0] 転置をとれば逆行列が求まるから 逆行列は [0, 0 , 1/3] [0,1/2, 0 ] [1, 0 , 0 ] |
行列式の定義 L:matrix([0,0,1],[0,2,0],[3,0,0]); [0,0,1] [0,2,0] [3,0,0] 行列式の計算 Ld:determinant(L); -6 逆行列の計算 L1:invert(L); [0, 0 , 1/3] [0,1/2, 0 ] [1, 0 , 0 ] |
[演習] [0,1,0] [1,0,0] の逆行列を求めよ。 [0,0,1] |
wxMaxima利用 |
行列式の計算 | 0,1,0 | | 1,0,0 |=-1 | 0,0,1 | 余因子 a11= 0,a12=1, a13=0 a21= 1,a22=0,a23=0 a31=0,a32=0, a33=-1 余因子行列 [0, -1, 0] [-1, 0, 0] [0, 0, 1] 転置をとれば逆行列が求まるから 逆行列は [0, -1 , 0 ] [-1, 0 , 0 ] [0, 0 , 1 ] |
行列式の定義 L:matrix([0,0,1],[0,2,0],[3,0,0]); [0,1,0] [1,0,0] [0,0,1] 行列式の計算 Ld:determinant(L); -1 逆行列の計算 L1:invert(L); [0, -1 , 0] [-1, 0 , 0] [0, 0 , 1] |
[演習] [0,0,1] [0,1,0] [1,2,3] [0,2,0]A[1,0,0]=[2,3,4] [3,0,0] [0,0,1] [3,4,5] を満たす行列Aを求めよ。 |
wxMaxima利用 |
[0,0,1] [0,2,0] [3,0,0] の逆行列は [0, 0 , 1/3] [0,1/2, 0 ] [1, 0 , 0 ] [0,1,0] [1,0,0] [0,0,1] の逆行列は [0, -1 , 0 ] [-1, 0 , 0 ] [0, 0 , 1 ] 従って A= [0, 0 , 1/3][0,0,1] [0,1,0][0, -1 , 0 ] [0, 0 , 1/3][1,2,3][0, -1 , 0 ] [0,1/2, 0 ][0,2,0]A[1,0,0][-1, 0 , 0 ]=[0,1/2, 0 ][2,3,4][-1, 0 , 0 ] [1, 0 , 0 ][3,0,0] [0,0,1][0, 0 , 1 ] [1, 0 , 0 ][3,4,5][0, 0 , 1 ] [4/3,1,5/3] =[3/2,1, 2 ] [ 2 ,1, 3 ] |
L:matrix([0,0,1],[0,2,0],[3,0,0]);Ld:determinant(L); R:matrix([0,1,0],[1,0,0],[0,0,1]);Rd:determinant(R); B:matrix([1,2,3],[2,3,4],[3,4,5]); matrix([0,0,1],[0,2,0],[3,0,0]) -6 matrix([0,1,0],[1,0,0],[0,0,1]) -1 matrix([1,2,3],[2,3,4],[3,4,5]) L1:invert(L);R1:invert(R); AA:L1.B.R1; matrix([0,0,1/3],[0,1/2,0],[1,0,0]) matrix([0,1,0],[1,0,0],[0,0,1]) matrix([4/3,1,5/3],[3/2,1,2],[2,1,3]) [確認] L.AA.R; matrix([1,2,3],[2,3,4],[3,4,5]) |
初版:2007.12.16
Update:2007.12.16
Update:2012.04.12