四阶行列式一共有几项组成？ 按照行列式的定义展开4阶行列式，共有多少项？为什么？
\u56db\u9636\u884c\u5217\u5f0f\u7684\u5b8c\u5168\u5c55\u5f00\u5f0f\u5171\u6709\u591a\u5c11\u9879\u56db\u9636\u884c\u5217\u5f0f\u7684\u5b8c\u5168\u5c55\u5f00\u5f0f\u5171\u670924\u9879\uff01\u8fc7\u7a0b\u5982\u4e0b\uff1a
1\u3001\u56db\u9636\u884c\u5217\u5f0f\u5c55\u5f00\uff0c\u5171\u67094\u4e2a\u4e0d\u540c\u7684\u4e09\u9636\u884c\u5217\u5f0f\uff1b
2\u3001\u6309\u3010\u884c\u5217\u5f0f\u5c55\u5f00\u5b9a\u7406\u3011,4\u9636\u884c\u5217\u5f0f\u5c55\u5f00\u6210\u4f4e\u4e00\u9636\u7684\u4e09\u9636\u884c\u5217\u5f0f\u65f6,\u6709\u56db\u4e2a\u5206\u884c\u5217\u5f0f\uff1b\u7ee7\u7eed\u3010\u5c55\u5f00\u3011\u4e0b\u53bb,\u6bcf\u4e2a3\u9636\u884c\u5217\u5f0f\u53ef\u4ee5\u3010\u5c55\u3011\u62103\u4e2a2\u9636\u884c\u5217\u5f0f\uff1b\u6bcf\u4e2a2\u9636\u884c\u5217\u5f0f\u53ef\u4ee5\u3010\u5c55\u3011\u62102\u9879.\u6240\u4ee5\u5168\u90e8\u5c55\u5f00\u540e\u5171\u6709 4!=24\u9879\u2014\u2014\u548c\u5b9a\u4e49\u63cf\u8ff0\u7684\u76f8\u540c!D4=a11A11+a12A12+a13A13+a14A14=a11M11-a12M12+a13M13-a14M14
\u62d3\u5c55\u8d44\u6599\uff1a
1\u3001\u6309\u7167\u4e00\u5b9a\u7684\u89c4\u5219\uff0c\u7531\u6392\u6210\u6b63\u65b9\u5f62\u7684\u4e00\u7ec4(n\u4e2a)\u6570(\u79f0\u4e3a\u5143\u7d20)\u4e4b\u4e58\u79ef\u5f62\u6210\u7684\u4ee3\u6570\u548c\uff0c\u79f0\u4e3an\u9636\u884c\u5217\u5f0f\u3002
\u4f8b\u5982\uff0c\u56db\u4e2a\u6570a\u3001b\u3001c\u3001d\u6240\u6392\u6210\u4e8c\u9636\u884c\u5f0f\u8bb0\u4e3a
\uff0c\u5b83\u7684\u5c55\u5f00\u5f0f\u4e3aad-bc\u3002
\u4e5d\u4e2a\u6570a1\uff0ca2\uff0ca3;b1\uff0cb2\uff0cb3;c1\uff0cc2\uff0cc3\u6392\u6210\u7684\u4e09\u9636\u884c\u5217\u5f0f\u8bb0\u4e3a
\uff0c\u5b83\u7684\u5c55\u5f00\u5f0f\u4e3aa1b2c3+a2b3c1+a3b1c2-a1b3c2-a2b1c3-a3b2c1\u3002
2\u3001\u884c\u5217\u5f0f\u8d77\u6e90\u4e8e\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u6c42\u89e3\uff0c\u5728\u6570\u5b66\u5404\u5206\u652f\u6709\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u5728\u4ee3\u6570\u4e0a\uff0c\u884c\u5217\u5f0f\u53ef\u7528\u6765\u7b80\u5316\u67d0\u4e9b\u8868\u8fbe\u5f0f\uff0c\u4f8b\u5982\u8868\u793a\u542b\u8f83\u5c11\u672a\u77e5\u6570\u7684\u7ebf\u6027\u65b9\u7a0b\u7ec4\u7684\u89e3\u7b49\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1\uff1an\u9636\u884c\u5217\u5f0f
\u6839\u636e\u5b9a\u4e49\uff1an\u9636\u884c\u5217\u5f0f\u7531n!\u4e2a\uff08n\u4e2a\u5143\u7d20\u4e58\u79ef\u7684\uff09\u9879\u7ec4\u6210\u3002\u6240\u4ee5 4 \u9636\u884c\u5217\u5f0f\u670924\u9879\u3002
3 阶是 3! = 3*2*1 = 6 项4 阶是 4! = 4*3*2*1 = 24 项
n 阶行列式有 n! = n(n-1)(n-2)...2*1 项
行列式是方阵 三阶的话就是3*3=9 4阶行列式就是16项了
三阶行列式是九项，四阶是十六项
n阶是n*n项
24项
=N!
绛旓細4 闃舵槸 4! = 4*3*2*1 = 24 椤 n 闃惰鍒楀紡鏈 n! = n(n-1)(n-2)...2*1 椤
绛旓細鍏24椤銆1.灏嗚琛屽垪寮忓墠涓夊垪閲嶅涔﹀啓鍦ㄨ琛屽垪寮忕殑鍙宠竟锛屽彲鍦ㄥ墠鍥涘垪涓綔鍑轰袱鏉″瑙掔嚎锛岀劧鍚庡湪姝や竷鍒椾腑浣滃嚭鐩稿簲鐨勫钩琛岀嚎锛屽彲寰(鍥捐〃涓)2.浣滀箻绉叧绯伙紝鍙緱濡備笅鍏」锛歛11a22a33a44,a12a23a34a41,a13a24a31a42,a14a21a32a43,a41a32a23a14,a42a33a24a11,a43a34a21a12,a44a31a22a13銆傝繖鍏」鐨勭鍙峰彲...
绛旓細鍥涢樁琛屽垪寮忓畬鍏ㄥ睍寮鏈24椤銆
绛旓細鍥涢樁琛屽垪寮忕殑瀹屽叏灞曞紑寮忓叡鏈24椤锛佽繃绋嬪涓嬶細1銆佸洓闃惰鍒楀紡灞曞紑锛屽叡鏈4涓笉鍚岀殑涓夐樁琛屽垪寮忥紱2銆佹寜銆愯鍒楀紡灞曞紑瀹氱悊銆,4闃惰鍒楀紡灞曞紑鎴愪綆涓闃剁殑涓夐樁琛屽垪寮忔椂,鏈夊洓涓垎琛屽垪寮忥紱缁х画銆愬睍寮銆戜笅鍘,姣忎釜3闃惰鍒楀紡鍙互銆愬睍銆戞垚3涓2闃惰鍒楀紡锛涙瘡涓2闃惰鍒楀紡鍙互銆愬睍銆戞垚2椤.鎵浠ュ叏閮ㄥ睍寮鍚庡叡鏈 4!=24椤...
绛旓細鍥涢樁琛屽垪寮忕殑瀹屽叏灞曞紑寮忓叡鏈24椤銆傚洓闃惰鍒楀紡灞曞紑锛屽叡鏈4涓笉鍚岀殑涓夐樁琛屽垪寮忋傛寜銆愯鍒楀紡灞曞紑瀹氱悊銆戯紝4闃惰鍒楀紡灞曞紑鎴愪綆涓闃剁殑涓夐樁琛屽垪寮忔椂锛屾湁鍥涗釜鍒嗚鍒楀紡锛涚户缁愬睍寮銆戜笅鍘伙紝姣忎釜3闃惰鍒楀紡鍙互銆愬睍銆戞垚3涓2闃惰鍒楀紡锛涙瘡涓2闃惰鍒楀紡鍙互銆愬睍銆戞垚2椤广傛墍浠ュ叏閮ㄥ睍寮鍚庡叡鏈 4!=24椤广傝鍒楀紡鍦ㄦ暟瀛...
绛旓細鍥涢樁琛屽垪寮忕殑灞曞紑寮忓叡鏈24椤銆傛嫇灞曪細灞曞紑鏂规硶鍙妌闃惰鍒楀紡鐨勫畾涔 鐢辨墍浣滃嚭鐨勫瑙掔嚎鍏崇郴鍙煡锛屽湪姣忎竴娆℃墍寰楃殑涔樼Н涓紝姣忎竴涓厓绱犲彧鑳芥湁涓ゆ潯绾跨粡杩囷紝鎵浠ワ紝涓涓厓绱犲彧鑳藉湪涓や釜涔樼Н涓嚭鐜帮紝鍏变綔涓夋鍥捐〃銆傛墍浠ュ彧鑳藉緱鍏」鍚湁璇ュ厓绱狅紝鍦╪闃惰鍒楀紡涓紝褰撻閫夋煇涓涓厓绱犱负鏌愪竴灞曞紑椤逛腑鐨勫厓绱犳椂锛屽叾浣欏厓绱犵殑...
绛旓細鎵鏈夐」锛屽叡鏈4锛=24椤锛屾瘡涓椤归兘鏄湁涓嶅悓琛屼笉鍚屽垪鐨4涓厓绱犵浉涔橈紝鐒跺悗涔樹互涓涓鍙凤紙閫嗗簭鏁板鍋舵у喅瀹氭璐燂級寰楀埌 娉ㄦ剰锛屽惈鏈夊厓绱0鐨勯」锛屽彲浠ョ洿鎺ョ渷鐣ャ
绛旓細鎵浠ヤ竴涓厓绱犲彧鑳藉湪涓や釜涔樼Н涓嚭鐜帮紝鍏变綔涓夋鍥捐〃锛屽彲浠ュ緱鍏」鍚湁璇ュ厓绱犮傚湪n闃惰鍒楀紡涓紝褰撻閫夋煇涓涓厓绱犱负鏌愪竴灞曞紑椤逛腑鐨勫厓绱犳椂锛屽叾浣欏厓绱犵殑閫夋嫨鍙兘浠庝綑涓嬬殑n-1闃跺瓙寮忎腑鍘婚夋嫨n-1涓厓绱犵粍鎴愯椤癸紝鏂规硶鏈(n-1)!绉嶃傚浜庡洓闃惰鍒楀紡鑰岃█鏈(4-1)!=6绉嶏紝鎵浠ユ寜涓婅堪鏂规硶灞曞紑鍚庡叡鏈24椤銆
绛旓細鍥涢樁琛屽垪寮涓紝鍚湁鍏冪礌 a31 鐨勯」锛鍏辨湁6椤癸紙灏辨槸a31鍜屽畠鐨勩婁唬鏁颁綑瀛愬紡銆婣31涔樼Н灞曞紑鍚庢墍寰楋級銆傚彲浠ユ牴鎹畾涔夆斺斿悇椤规墍鍚厓绱犮愪笉鍚岃&涓嶅悓鍒椼戞妸瀹冧滑鍐欏嚭鏉ワ細a12a23a31a44銆乤13a22a31a44銆乤14a23a31a42銆乤12a24a31a43銆乤13a24a31a42銆乤14a22a31a43,鐒跺悗鍒嗗埆璁＄畻瀹冧滑鐨勯嗗簭鏁帮紝鎸夈婂璐熷伓姝ｃ...
绛旓細鍦4闃惰鍒楀紡涓紝鍚玜13,a14鐨勯」鏈塧13A13+a14A14,鍏朵腑A13锛孉14鏄痑13,a14鐨勪唬鏁颁綑瀛愬紡锛孉13锛孉14鏄3闃惰鍒楀紡锛屽睍寮鍚庡悇鏈6椤癸紝鎵浠ュ畠浠鍏辨湁12椤广
