4阶行列式计算公式 四阶行列式简单计算方法
\u56db\u9636\u884c\u5217\u5f0f\u600e\u4e48\u8ba1\u7b97?\u56db\u9636\u884c\u5217\u5f0f\u7684\u8ba1\u7b97\u65b9\u6cd5\uff1a
\u7b2c1\u6b65\uff1a\u628a2\u30013\u30014\u5217\u52a0\u5230\u7b2c1 \u5217\uff0c\u63d0\u51fa\u7b2c1\u5217\u516c\u56e0\u5b50 10\uff0c\u5316\u4e3a
1 2 3 4
1 3 4 1
1 4 1 2
1 1 2 3
\u7b2c2\u6b65\uff1a\u7b2c1\u884c\u4e58 -1 \u52a0\u5230\u5176\u4f59\u5404\u884c\uff0c\u5f97
1 2 3 4
0 1 1 -3
0 2 -2 -2
0 -1 -1 -1
\u7b2c3\u6b65\uff1ar3 - 2r1,r4+r1\uff0c\u5f97
1 2 3 4
0 1 1 -3
0 0 -4 4
0 0 0 -4
\u6240\u4ee5\u884c\u5217\u5f0f = 10* (-4)*(-4) = 160\u3002
\u6269\u5c55\u8d44\u6599
\u56db\u9636\u884c\u5217\u5f0f\u7684\u6027\u8d28
1\u3001\u5728 n \u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\uff0c\u884c\u5217\u5f0f\u63cf\u8ff0\u7684\u662f\u4e00\u4e2a\u7ebf\u6027\u53d8\u6362\u5bf9\u201c\u4f53\u79ef\u201d\u6240\u9020\u6210\u7684\u5f71\u54cd\u3002
2\u3001\u884c\u5217\u5f0fA\u7b49\u4e8e\u5176\u8f6c\u7f6e\u884c\u5217\u5f0fAT(AT\u7684\u7b2ci\u884c\u4e3aA\u7684\u7b2ci\u5217)\u3002
3\u3001\u56db\u9636\u884c\u5217\u5f0f\u7531\u6392\u6210n\u9636\u65b9\u9635\u5f62\u5f0f\u7684n²\u4e2a\u6570aij(i,j=1,2,...,n)\u786e\u5b9a\u7684\u4e00\u4e2a\u6570\uff0c\u5176\u503c\u4e3an\u3002
4\u3001\u56db\u9636\u884c\u5217\u5f0f\u4e2dk1,k2,...,kn\u662f\u5c06\u5e8f\u52171,2,...,n\u7684\u5143\u7d20\u6b21\u5e8f\u4ea4\u6362k\u6b21\u6240\u5f97\u5230\u7684\u4e00\u4e2a\u5e8f\u5217\uff0c\u03a3\u53f7\u8868\u793a\u5bf9k1,k2,...,kn\u53d6\u904d1,2,...,n\u7684\u4e00\u5207\u6392\u5217\u6c42\u548c\uff0c\u90a3\u4e48\u6570D\u79f0\u4e3an\u9636\u65b9\u9635\u76f8\u5e94\u7684\u884c\u5217\u5f0f\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\u2014\u884c\u5217\u5f0f
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4阶行列式计算公式是(a1b2-a2b1)(c3d4-c4d3)-(a1b3-a3b1)(c2d4-c4d2)+(a1b4-a4b1)(c2d3-c3d2)+(a2b3-a3b2)(c1d4-c4d1)-(a2b4-a4b2绛旓細鍥涢樁琛屽垪寮忕殑鍏紡鏄細D4=a11a22a33a44-a12a23a34a41+a13a24a31a42-a14a21a32a43+a41a32a23a14-a42a33a24a11+a43a34a21a12-a44a31a22a13+a11a23a34a42-a13a24a32a41+a14a22a31a43-a12a21a33a44+a41a33a24a12- a43a34a22a11+a14a32a21a13-a42a31a23a14+a11a24a32a43-a14a22a33a41+a12a23...
绛旓細鍥涢樁琛屽垪寮忎竾鑳藉叕寮忓涓嬶細a11 a12 a13 a14 a21 a22 a23 a24 a31 a32 a33 a34 a41 a42 a43 a44= a11a22a33a44 - a11a22a34a43 - a11a23a32a44 + a11a23a34a42+ a11a24a32a43 - a11a24a33a42 - a12a21a33a44 + a12a21a34a43+ a12a23a31a44 - a12a23a34a41 - a12a24a31a43 + a1...
绛旓細D = a_{11}D_{11} - a_{12}D_{12} + a_{13}D_{13} - a_{14}D_{14} 鍏朵腑锛$D_{11}$銆$D_{12}$銆$D_{13}$鍜$D_{14}$鍒嗗埆鏄皢鍘熻鍒楀紡鐨勭涓琛屽垹闄ゅ悗锛屽緱鍒扮殑浠$a_{11}$銆$a_{12}$銆$a_{13}$鍜$a_{14}$涓哄乏涓婅鍏冪礌鐨勪笁闃惰鍒楀紡銆傛帴涓嬫潵锛屾垜浠彲浠ョ户缁...
绛旓細4闃惰鍒楀紡璁＄畻鍏紡鏄(a1b2-a2b1)(c3d4-c4d3)-(a1b3-a3b1)(c2d4-c4d2)+(a1b4-a4b1)(c2d3-c3d2)+(a2b3-a3b2)(c1d4-c4d1)-(a2b4-a4b2
绛旓細鍥涢樁琛屽垪寮鐨璁＄畻鏂规硶锛氱1姝ワ細鎶2銆3銆4鍒楀姞鍒扮1 鍒楋紝鎻愬嚭绗1鍒楀叕鍥犲瓙 10锛屽寲涓 1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 绗2姝ワ細绗1琛屼箻 -1 鍔犲埌鍏朵綑鍚勮锛屽緱 1 2 3 4 0 1 1 -3 0 2 -2 -2 0 -1 -1 -1 绗3姝ワ細r3 - 2r1,r4+r1锛屽緱 1 2 3 4 0 1 1 -...
绛旓細鍥涢樁琛屽垪寮鐨璁＄畻鍏紡濡備笅锛氣垼 𝑎1 ,1 𝑎1 ,2 𝑎1 ,3 𝑎1 ,4 𝑎2 ,1 𝑎2 ,2 𝑎2 ,3 𝑎2 ,4 𝑎3 ,1 𝑎3 ,2 𝑎3 ,3 𝑎3 ,4 𝑎4 ,1 𝑎4 ,2 𝑎4 ,...
绛旓細娌℃湁璁＄畻鍏紡锛屽彧鏈夐氱敤璁＄畻鏂规硶锛鍥涢樁琛屽垪寮鐨勮绠楁柟娉曪細绗1姝ワ細鎶2銆3銆4鍒楀姞鍒扮1鍒楋紝鎻愬嚭绗1鍒楀叕鍥犲瓙10锛屽寲涓猴細1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 绗2姝ワ細绗1琛屼箻锛-1锛夊姞鍒板叾浣欏悇琛岋紝寰楋細1 2 3 4 0 1 1 -3 0 2 -2 -2 0 -1 -1 -1 绗3姝ワ細r3 - 2r1,r4...
绛旓細0 5 -4 0 0 -5 0 -3 绗3琛屽姞涓婄4琛岋紝绗4琛屽噺鍘荤2琛 = 1 0 3 2 0 -5 -6 -4 0 0 -4 -3 0 0 6 1 绗4琛屽姞涓婄3琛屆1.5 = 1 0 3 2 0 -5 -6 -4 0 0 -4 -3 0 0 0 -3.5 寰楀埌浜嗕笁瑙掑舰琛屽垪寮 =1*(-5)*(-4)*(-3.5...
绛旓細2銆佽鍒楀紡A绛変簬鍏惰浆缃鍒楀紡AT(AT鐨勭i琛屼负A鐨勭i鍒)銆3銆鍥涢樁琛屽垪寮鐢辨帓鎴恘闃舵柟闃靛舰寮忕殑n²涓暟aij(i,j=1,2,...,n)纭畾鐨勪竴涓暟锛屽叾鍊间负n銆4銆佸洓闃惰鍒楀紡涓璳1,k2,...,kn鏄皢搴忓垪1,2,...,n鐨勫厓绱犳搴忎氦鎹娆℃墍寰楀埌鐨勪竴涓簭鍒楋紝危鍙疯〃绀哄k1,k2,...,kn鍙栭亶1,2,...,...
绛旓細4闃惰鍒楀紡鐨璁＄畻鏂规硶锛氱1姝ワ細鎶2銆3銆4鍒楀姞鍒扮1 鍒楋紝鎻愬嚭绗1鍒楀叕鍥犲瓙 10锛屽寲涓 1 2 3 4 1 3 4 1 1 4 1 2 1 1 2 3 绗2姝ワ細绗1琛屼箻 -1 鍔犲埌鍏朵綑鍚勮锛屽緱 1 2 3 4 0 1 1 -3 0 2 -2 -2 0 -1 -1 -1 绗3姝ワ細r3 - 2r1,r4+r1锛屽緱 1 2 3 4 0 1 1 -...
