求下列矩阵的逆矩阵，要详细过程，谢谢 1 2 3 2 3 4 4 1 2 求矩阵[1 3 2，0 -1 4,2 1 3]的逆矩阵，详细...

\u521d\u7b49\u53d8\u5e7b\u9006\u77e9\u9635 1 2 3 4 2 3 1 2 1 1 1 -1 1 0 -2 -6 \u7528\u521d\u7b49\u884c\u53d8\u6362\u6c42\u9006\u77e9\u9635 \uff0c\u8981\u8be6\u7ec6\u8fc7\u7a0b

\u7528\u521d\u7b49\u884c\u53d8\u5316\u6c42\u77e9\u9635\u7684\u9006\u77e9\u9635\u7684\u65f6\u5019\uff0c
\u5373\u7528\u884c\u53d8\u6362\u628a\u77e9\u9635(A\uff0cE)\u5316\u6210(E\uff0cB)\u7684\u5f62\u5f0f\uff0c\u90a3\u4e48B\u5c31\u7b49\u4e8eA\u7684\u9006
\u5728\u8fd9\u91cc
(A\uff0cE)=
1 2 3 4 1 0 0 0
2 3 1 2 0 1 0 0
1 1 1 -1 0 0 1 0
1 0 -2 -6 0 0 0 1 \u7b2c1\u884c\u51cf\u53bb\u7b2c3\u884c\uff0c \u7b2c2\u884c\u51cf\u53bb\u7b2c3\u884c\u00d72\uff0c\u7b2c3\u884c\u51cf\u53bb\u7b2c4\u884c
\uff5e
0 1 2 5 1 0 -1 0
0 1 -1 4 0 1 -2 0
0 1 3 5 0 0 1 -1
1 0 -2 -6 0 0 0 1 \u7b2c3\u884c\u51cf\u53bb\u7b2c1\u884c\uff0c\u7b2c1\u884c\u51cf\u53bb\u7b2c2\u884c
\uff5e
0 0 3 1 1 -1 1 0
0 1 -1 4 0 1 -2 0
0 0 1 0 -1 0 2 -1
1 0 -2 -6 0 0 0 1 \u7b2c1\u884c\u51cf\u53bb\u7b2c3\u884c\u00d73\uff0c\u7b2c2\u884c\u52a0\u4e0a\u7b2c3\u884c\uff0c\u7b2c4\u884c\u52a0\u4e0a\u7b2c3\u884c\u00d72
\uff5e
0 0 0 1 4 -1 -5 3
0 1 0 4 -1 1 0 -1
0 0 1 0 -1 0 2 -1
1 0 0 -6 -2 0 4 -1 \u7b2c2\u884c\u51cf\u53bb\u7b2c1\u884c\u00d74\uff0c\u7b2c4\u884c\u52a0\u4e0a\u7b2c1\u884c\u00d76
\uff5e
0 0 0 1 4 -1 -5 3
0 1 0 0 -17 5 20 -13
0 0 1 0 -1 0 2 -1
1 0 0 0 22 -6 -26 17 \u4ea4\u6362\u7b2c1\u884c\u548c\u7b2c4\u884c
\uff5e
1 0 0 0 22 -6 -26 17
0 1 0 0 -17 5 20 -13
0 0 1 0 -1 0 2 -1
0 0 0 1 4 -1 -5 3
=( E,A^(-1) )

\u8fd9\u6837\u5c31\u5df2\u7ecf\u901a\u8fc7\u521d\u7b49\u884c\u53d8\u6362\u628a(A,E)\uff5e(E,A^-1)

\u4e8e\u662f\u5f97\u5230\u4e86\u539f\u77e9\u9635\u7684\u9006\u77e9\u9635\u5c31\u662f
22 -6 -26 17
-17 5 20 -13
-1 0 2 -1
4 -1 -5 3

\u7528\u521d\u7b49\u884c\u53d8\u5316\u6c42\u77e9\u9635\u7684\u9006\u77e9\u9635\u7684\u65f6\u5019\uff0c
\u5373\u7528\u884c\u53d8\u6362\u628a\u77e9\u9635(A\uff0cE)\u5316\u6210(E\uff0cB)\u7684\u5f62\u5f0f\uff0c\u90a3\u4e48B\u5c31\u7b49\u4e8eA\u7684\u9006
\u5728\u8fd9\u91cc
(A\uff0cE)=
1 3 2 1 0 0
0 -1 4 0 1 0
2 1 3 0 0 1 r1+3r2\uff0cr3+r2,r2*(-1)
\uff5e
1 0 14 1 3 0
0 1 -4 0 -1 0
2 0 7 0 1 1 r3-2r1,r3/(-21)
~
1 0 14 1 3 0
0 1 -4 0 -1 0
0 0 1 2/21 5/21 -1/21 r1-14r3,r2+4r3
~
1 0 0 -1/3 -1/3 2/3
0 1 0 8/21 -1/21 -4/21
0 0 1 2/21 5/21 -1/21
\u8fd9\u6837\u5c31\u5df2\u7ecf\u901a\u8fc7\u521d\u7b49\u884c\u53d8\u6362\u628a(A,E)\uff5e(E,A^-1)
\u4e8e\u662f\u5f97\u5230\u4e86\u539f\u77e9\u9635\u7684\u9006\u77e9\u9635\u5c31\u662f
-1/3 -1/3 2/3
8/21 -1/21 -4/21
2/21 5/21 -1/21

用初等行变化求矩阵的逆矩阵的时候，
即用行变换把矩阵(A，E)化成(E，B)的形式，那么B就等于A的逆
在这里
(A，E)=
1 2 3 1 0 0
2 3 4 0 1 0
4 1 2 0 0 1 r3-2r2，r2-2r1
～
1 2 3 1 0 0
0 -1 -2 -2 1 0
0 -5 -6 0 -2 1 r1+2r2，r3-5r2，r2*(-1)
～
1 0 -1 -3 2 0
0 1 2 2 -1 0
0 0 4 10 -7 1 r3 /4，r1+r3，r2-2r3
～
1 0 0 -1/2 1/4 1/4
0 1 0 -3 5/2 -1/2
0 0 1 5/2 -7/4 1/4
这样就已经通过初等行变换把(A,E)～(E,A^-1)
于是得到了原矩阵的逆矩阵就是
-1/2 1/4 1/4
-3 5/2 -1/2
5/2 -7/4 1/4

姹傞嗙煩闃,瑕佽缁嗚繃绋
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绛旓細[ A | E ] = 1 2 3 4 1 0 0 0 2 3 1 2 0 1 0 0 1 1 1 -1

姹涓閫嗙煩闃
绛旓細3.鏍规嵁浣犵殑瑕佹眰寤虹珛鐭╅樀绯荤粺(鍥句腑渚嬪瓙璁剧煩闃礎=[1,2,3,4]锛屸楢鈥欏彲浠ュ畾涔変负浣闇瑕佺殑浠讳綍瀛楁瘝)濡備笅鍥炬墍绀恒4.浣跨敤浠ｇ爜B=inv(A)锛屸淏鈥濆彲浠ュ畾涔変负鎮ㄩ渶瑕佺殑鍏朵粬瀛楁瘝锛宨nv()涓殑瀛楁瘝鏄偍闇瑕佸弽杞殑鐭╅樀锛屽涓鍥炬墍绀恒5.楠岃瘉瑙鐨勯锛屽鏋滀袱涓鐭╅樀鐨涔樼Н鏄崟浣嶇煩闃碉紝鍒欏叾閫嗘槸姝ｇ‘鐨勶紝濡備笅鍥炬墍绀...

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绛旓細瑙: (A,E)= 1 2 3 1 0 0 2 1 2 0 1 0 1 3 3 0 0 1 r2-2r1,r3-r1 1 2 3 1 0 0 0 -3 -4 -2 1 0 0 1 0 -1 0 1 r1-2r3,r2+3r3 1 0 3 3 0 -2 0 0 -4 -5 1 3 0 1 0 -1 0 1 r2*(...

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