三阶行列式的简便运算公式是什么？ 三阶行列式计算方法
\u4e09\u9636\u884c\u5217\u5f0f\u8ba1\u7b97\u65b9\u6cd5\u662f\u4ec0\u4e48\uff1f\u4e09\u9636\u884c\u5217\u5f0f\u8ba1\u7b97\u65b9\u6cd5\uff0c\u5982\u4e0b\uff1a
\u8fd9\u91cc\u4e00\u5171\u662f\u516d\u9879\u76f8\u52a0\u51cf\uff0c\u6574\u7406\u4e0b\u53ef\u4ee5\u8fd9\u4e48\u8bb0\uff1a
a1(b2\u00b7c3-b3\u00b7c2) - a2(b1\u00b7c3-b3\u00b7c1) + a3(b1\u00b7c2-b2\u00b7c1)=
a1(b2\u00b7c3-b3\u00b7c2) - b1(a2\u00b7c3 - a3\u00b7c2) + c1(a2\u00b7b3 - a3\u00b7b2)
\u6b64\u65f6\u53ef\u4ee5\u8bb0\u4f4f\u4e3a\uff1a
a1*(a1\u7684\u4f59\u5b50\u5f0f)-a2*(a2\u7684\u4f59\u5b50\u5f0f)+a3*(a3\u7684\u4f59\u5b50\u5f0f)=
a1*(a1\u7684\u4f59\u5b50\u5f0f)-b1*(b1\u7684\u4f59\u5b50\u5f0f)+c1*(c1\u7684\u4f59\u5b50\u5f0f)
\u4e09\u9636\u884c\u5217\u5f0f\u7684\u6027\u8d28
\u6027\u8d281\uff1a\u884c\u5217\u5f0f\u4e0e\u5b83\u7684\u8f6c\u7f6e\u884c\u5217\u5f0f\u76f8\u7b49\u3002
\u6027\u8d282\uff1a\u4e92\u6362\u884c\u5217\u5f0f\u7684\u4e24\u884c(\u5217)\uff0c\u884c\u5217\u5f0f\u53d8\u53f7\u3002
\u63a8\u8bba\uff1a\u5982\u679c\u884c\u5217\u5f0f\u6709\u4e24\u884c(\u5217)\u5b8c\u5168\u76f8\u540c\uff0c\u5219\u6b64\u884c\u5217\u5f0f\u4e3a\u96f6\u3002
\u6027\u8d283\uff1a\u884c\u5217\u5f0f\u7684\u67d0\u4e00\u884c(\u5217)\u4e2d\u6240\u6709\u7684\u5143\u7d20\u90fd\u4e58\u4ee5\u540c\u4e00\u6570k\uff0c\u7b49\u4e8e\u7528\u6570k\u4e58\u6b64\u884c\u5217\u5f0f\u3002
\u63a8\u8bba\uff1a\u884c\u5217\u5f0f\u4e2d\u67d0\u4e00\u884c(\u5217)\u7684\u6240\u6709\u5143\u7d20\u7684\u516c\u56e0\u5b50\u53ef\u4ee5\u63d0\u5230\u884c\u5217\u5f0f\u7b26\u53f7\u7684\u5916\u9762\u3002
\u6027\u8d284\uff1a\u884c\u5217\u5f0f\u4e2d\u5982\u679c\u6709\u4e24\u884c(\u5217)\u5143\u7d20\u6210\u6bd4\u4f8b\uff0c\u5219\u6b64\u884c\u5217\u5f0f\u7b49\u4e8e\u96f6\u3002
\u6027\u8d285\uff1a\u628a\u884c\u5217\u5f0f\u7684\u67d0\u4e00\u5217(\u884c)\u7684\u5404\u5143\u7d20\u4e58\u4ee5\u540c\u4e00\u6570\u7136\u540e\u52a0\u5230\u53e6\u4e00\u5217(\u884c)\u5bf9\u5e94\u7684\u5143\u7d20\u4e0a\u53bb\uff0c\u884c\u5217\u5f0f\u4e0d\u53d8\u3002
D = a11a22a33 + a12a23a31 + a13a21a32
- a13a22a31 - a12a21a33 - a11a23a32
绛旓細涓夐樁琛屽垪寮忓彲鐢ㄥ瑙掔嚎娉曞垯D = a11a22a33 + a12a23a31 + a13a21a32 - a13a22a31 - a12a21a33 - a11a23a32 鐪嬪浘鍔╄: http://hiphotos.baidu.com/lry31383/pic/item/ae808adbe581da7811df9b9f.jpg
绛旓細涓夐樁琛屽垪寮忓彲鐢ㄥ瑙掔嚎娉曞垯锛D = a11a22a33 + a12a23a31 + a13a21a32- a13a22a31 - a12a21a33 - a11a23a32銆傜煩闃礎涔樼煩闃礏锛屽緱鐭╅樀C锛屾柟娉曟槸A鐨勭涓琛屽厓绱犲垎鍒搴斾箻浠鐨勭涓鍒楀厓绱犲悇鍏冪礌锛岀浉鍔犲緱C11锛孉鐨勭涓琛屽厓绱犲搴斾箻浠鐨勭浜岃鍚勫厓绱狅紝鐩稿姞寰桟12锛孋鐨勭浜岃鍏冪礌涓篈鐨勭浜岃鍏冪礌鎸...
绛旓細涓夐樁琛屽垪寮忓彲鐢ㄥ瑙掔嚎娉曞垯锛D = a11a22a33 + a12a23a31 + a13a21a32- a13a22a31 - a12a21a33 - a11a23a32銆倈a11 a12 a13|=a11a22a33-a11a23a32+a12a23a31-a12a21a33+a13a32a21-a13a22a31锛宎21 a22 a23銆俛31 a32 a33锛=a11a22a33+a12a23a31+a13a21a32-a11a23a32-a12a21a33-a13a22a31...
绛旓細涓夐樁琛屽垪寮忚绠楁柟娉曪紝濡備笅锛氳繖閲屼竴鍏辨槸鍏」鐩稿姞鍑忥紝鏁寸悊涓嬪彲浠ヨ繖涔堣锛a1(b2路c3-b3路c2) - a2(b1路c3-b3路c1) + a3(b1路c2-b2路c1)=a1(b2路c3-b3路c2) - b1(a2路c3 - a3路c2) + c1(a2路b3 - a3路b2)銆傛鏃跺彲浠ヨ浣忎负锛歛1*(a1鐨勪綑瀛愬紡)-a2*(a2鐨勪綑瀛愬紡)+a3*(a3鐨勪綑瀛...
绛旓細涓夐樁琛屽垪寮璁＄畻鏂规硶锛屽鍥炬墍绀猴細涓轰簡瀹规槗璁颁綇鍏舵眰瑙ｅ叕寮忥紝浣嗚璁颁綇杩欎釜姹傝В鍏紡鏄寰堝洶闅剧殑锛屽洜姝ゅ紩鍏涓夐樁琛屽垪寮忕殑姒傚康銆傛爣鍑嗘柟娉曟槸鍦ㄥ凡缁欒鍒楀紡鐨勫彸杈规坊鍔犲凡缁欒鍒楀紡鐨勭涓鍒椼佺浜屽垪銆傛垜浠妸琛屽垪寮忕殑宸︿笂瑙掑埌鍙充笅瑙掔殑瀵硅绾跨О涓轰富瀵硅绾匡紝鎶婂彸涓婅鍒板乏涓嬭鐨勫瑙掔嚎绉颁负娆″瑙掔嚎銆傝繖鏃讹紝涓夐樁琛屽垪寮忕殑鍊...
绛旓細涓夐樁琛屽垪寮忔槸绾挎т唬鏁颁腑涓涓噸瑕佺殑姒傚康锛屽浜庡畠鐨璁＄畻鍏紡銆傚叾鐩稿叧瑙ｉ噴濡備笅锛1銆佸亣璁炬垜浠湁涓涓笁闃惰鍒楀紡锛屽畠鐨勫厓绱犲垎鍒槸a_i,j锛坕琛ㄧず琛岋紝j琛ㄧず鍒楋級锛岄偅涔堣繖涓琛屽垪寮忕殑鍊煎彲浠ラ氳繃浠ヤ笅鍏紡璁＄畻锛欴=a_11*锛坅_22*a_33-a_32*a_23锛+a_12*锛坅_23*a_31-a_32*a_21锛+a_13*锛坅_21*a_...
绛旓細涓夐樁琛屽垪寮忓彲鐢ㄥ瑙掔嚎娉曞垯锛欴 = a11a22a33 + a12a23a31 + a13a21a32- a13a22a31 - a12a21a33 - a11a23a32銆倈a11 a12 a13|=a11a22a33-a11a23a32+a12a23a31-a12a21a33+a13a32a21-a13a22a31锛宎21 a22 a23銆俛31 a32 a33锛=a11a22a33+a12a23a31+a13a21a32-a11a23a32-a12a21a33-a13a22a31...
绛旓細涓夐樁琛屽垪寮忓彲鐢ㄥ瑙掔嚎娉曞垯:D = a11a22a33 + a12a23a31 + a13a21a32- a13a22a31 - a12a21a33 - a11a23a32 鐢ㄥ瑙掔嚎娉曞垯濡傚浘:
绛旓細A = [[a, b, c],[d, e, f],[g, h, i]]鍏跺搴旂殑涓夐樁琛屽垪寮忕殑灞曞紑寮忎负锛殀A| = aei + bfg + cdh - ceg - bdi - afh 涓夎褰㈡硶锛圫arrus娉曞垯锛夋槸鍙︿竴绉嶇敤浜璁＄畻涓夐樁琛屽垪寮忕殑鏂规硶锛屽叾姝ラ濡備笅锛1. 灏3x3鐭╅樀澶嶅埗涓ゆ骞跺皢鍏剁矘璐村埌鍙充晶锛屽舰鎴愪簡涓涓6x3鐨勭煩闃点2. 浠庡乏涓婅鍒板彸涓...
绛旓細涓夐樁琛屽垪寮璁＄畻鏂规硶锛屽鍥炬墍绀猴細涓轰簡瀹规槗璁颁綇鍏舵眰瑙ｅ叕寮忥紝浣嗚璁颁綇杩欎釜姹傝В鍏紡鏄寰堝洶闅剧殑锛屽洜姝ゅ紩鍏涓夐樁琛屽垪寮忕殑姒傚康銆傛爣鍑嗘柟娉曟槸鍦ㄥ凡缁欒鍒楀紡鐨勫彸杈规坊鍔犲凡缁欒鍒楀紡鐨勭涓鍒椼佺浜屽垪銆傛垜浠妸琛屽垪寮忕殑宸︿笂瑙掑埌鍙充笅瑙掔殑瀵硅绾跨О涓轰富瀵硅绾匡紝鎶婂彸涓婅鍒板乏涓嬭鐨勫瑙掔嚎绉颁负娆″瑙掔嚎銆傝繖鏃讹紝涓夐樁琛屽垪寮忕殑鍊...
