行列式化简
\u7ebf\u6027\u4ee3\u6570\u884c\u5217\u5f0f\u5316\u7b80\u7684\u95ee\u9898\u7b2c\u4e00\u4e2a\u7b49\u5f0f\uff1a\u662f\u540e\u97623\u5217\u5168\u90e8\u52a0\u5230\u7b2c\u4e00\u5217\uff0c\u884c\u5217\u5f0f\u503c\u4e0d\u53d8\uff1b
\u7b2c\u4e8c\u4e2a\u7b49\u5f0f\uff1a\u63d0\u53d6\u7b2c\u4e00\u5217\u516c\u5171\u56e0\u5f0f\uff08a+3b\uff09\uff0c\u884c\u5217\u5f0f\u503c\u4e0d\u53d8\uff1b
\u6700\u540e\u4e00\u4e2a\u7b49\u5f0f\uff1a\u5c31\u662f\u6309\u6b65\u9aa4\u5316\u7b80\u4e86\uff0c\u57fa\u7840\u6b65\u9aa4\u90fd\u662f
\u671b\u91c7\u7eb3
\u4e00\u822c\u8981\u770b\u5177\u4f53\u7684\u6570\u636e\u7ed3\u6784
\u4f60\u770b\u770b\u8fd9\u4e2a\u4f8b\u5b50\u5427
http://zhidao.baidu.com/question/319559808.html
如下
绛旓細鍏堟寜瀹氫箟鍐欏嚭琛屽垪寮鐨勫悇鍏冪礌锛岀劧鍚庡啀鍒╃敤琛屽垪寮忕殑鎬ц川鍖栦负涓嬩笁瑙掕鍒楀紡銆備笅鍥剧殑璁＄畻杩囩▼涓庣瓟妗堜唬鍙傝冦傜煩闃佃鍒楀紡鏄寚鐭╅樀鐨勫叏閮ㄥ厓绱犳瀯鎴愮殑琛屽垪寮忥紝璁続=(aij)鏄暟鍩烶涓婄殑涓涓猲闃剁煩闃碉紝鍒欐墍鏈堿=(aij)涓殑鍏冪礌缁勬垚鐨勮鍒楀紡绉颁负鐭╅樀A鐨勮鍒楀紡锛岃涓簗A|鎴杁et(A)銆傝嫢A锛孊鏄暟鍩烶涓婄殑涓や釜n闃剁煩闃碉紝k鏄...
绛旓細璇ュ紡瀛愪笉鍙互鐩存帴闄ゆ暟銆琛屽垪寮忓寲绠鍙埄鐢ㄨ鍒楀紡灞曞紑瀹氱悊闄嶉樁锛岀煩闃典竴鑸敤琛屽彉鎹紝鍙湁鐗规畩鎯呭喌鎵嶇敤鍒楀彉鎹傚湪璇ュ寲绠杩囩▼涓紝鍙兘鍖栫畝琛屽垪寮忥紝涓嶈兘鐩存帴鐢ㄨ绠楁満鍒楀紡鎴栬呯洿鎺ラ櫎鏁般傚叾瀹氫箟鍩熶负det鐨勭煩闃礎锛屽彇鍊间负涓涓爣閲忥紝鍐欎綔det(A)鎴東A|銆
绛旓細鍙樺舰鍚庢垚涓嬩笁瑙掑舰鏍峰紡锛屽壇瀵硅绾夸箻绉紝绗﹀彿(-1)³鏂规硶濡備笅鍥炬墍绀猴紝璇蜂綔鍙傝冿紝绁濆涔犳剦蹇細
绛旓細琛屽垪寮忓寲绠鍙埄鐢ㄨ鍒楀紡灞曞紑瀹氱悊闄嶉樁锛岀煩闃典竴鑸敤琛屽彉鎹紝鍙湁鐗规畩鎯呭喌鎵嶇敤鍒楀彉鎹傝鍒楀紡鍦ㄦ暟瀛︿腑锛屾槸涓涓嚱鏁帮紝鍏跺畾涔夊煙涓篸et鐨勭煩闃礎锛屽彇鍊间负涓涓爣閲忥紝鍐欎綔det(A)鎴東A|銆傛棤璁烘槸鍦ㄧ嚎鎬т唬鏁般佸椤瑰紡鐞嗚锛岃繕鏄湪寰Н鍒嗗涓紙姣斿璇存崲鍏冪Н鍒嗘硶涓級锛岃鍒楀紡浣滀负鍩烘湰鐨勬暟瀛﹀伐鍏凤紝閮芥湁鐫閲嶈鐨勫簲鐢ㄣ傝鍒楀紡...
绛旓細鍙互灏嗘煇涓琛屾垨鏌愪竴鍒楀寲涓洪櫎涓涓厓绱犲鍏跺畠閮戒负0锛岀劧鍚庢寜閭ｄ竴琛岋紙鎴栭偅涓鍒楋級灞曞紑銆備緥濡傦細浣滃彉鎹 r1=r1-5r2锛況3=r3-3r2锛況4=r4-2r2锛屽師琛屽垪寮鍖栦负 -33 0 -23 -21 8 1 6 6 -18 0 -13 -11 -11 0 -11 -9鎸夌浜屽垪灞曞紑锛屽緱銆愬悇琛屾彁涓涓-1锛...
绛旓細鍙互褰掔撼璇佹槑锛屽厛鑰冭檻D涓1鍒椼傝嫢绗1鍒椾腑鍏冪礌閮芥槸0锛屽垯琛屽垪寮绛変簬0銆傚惁鍒欙紝灏嗕竴涓潪闆跺厓浜ゆ崲鍒板乏涓婅锛岀敤瀹冨皢绗1鍒椾腑鍏朵綑鍏冪礌鍖栦负0銆傝嚦姝わ紝D鐨勭1琛屼笌绗1鍒楀氨涓嶇敤鍔ㄤ簡銆傦紙鐩稿綋浜庤鍒楀紡闄嶄簡涓闃讹級鐢ㄥ悓鏍风殑鏂规硶澶勭悊绗2鍒椼傚姝や笅鍘伙紝琛屽垪寮忓彲鍖栦负涓涓笂涓夎琛屽垪寮忋備妇渚嬶細n闃惰鍒楀紡鍖栦笁瑙掑紡D...
绛旓細濡備笅
绛旓細鎶婄涓鑷崇n-1琛岄兘鍔犲埌绗琻琛岋紝绗琻琛岀殑鍏冪礌閮藉彉涓0.鍐嶆妸绗竴鑷崇n-1鍒楅兘鍑忓幓绗琻鍒楋紝鍓峮-1鍒楃殑涓诲瑙掔嚎涓婄殑鍏冪礌鏄-n,姝ゅ閮芥槸0.鎻愬嚭(-n),骞舵妸绗琻鍒椾箻浠-1锛屽氨寰楀埌鍙宠竟鐨琛屽垪寮銆
绛旓細1:鍏-1=鍏-1+(-9+-9+-9)=鍏-1+锛-9.3锛夈(鍏-1)+-27:鍏=27 2:鍏-1 = 3:鍏-1= 4:鍏-1= 瑙夊緱鎴戜簺鐨勫ソ灏辩偣涓禐鍚
绛旓細绗3鍒楋紝鍑忓幓绗2鍒楋紝寰楀埌 (c-b)(d-b)1 0 0 a+b 1 0 0 (a+c)(c+b) (a+d)(d+b)-(a+c)(c+b)寰楀埌涓嬩笁瑙琛屽垪寮锛屼富瀵硅绾垮厓绱犵浉涔橈紝寰楀埌 (c-b)(d-b)[(a+d)(d+b)-(a+c)(c+b)]=(c-b)(d-b)(ad+d^2+bd-ac-c^2-bc)=(c-b)(d-b)(d-c)(a+b+c+d)...
