一个矩阵以数k≠0乘某一行的所有元素后与原来的矩阵相等吗 矩阵初等变换中<以数k(k不为0)乘某一行中所有元素;>与其...
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两个矩阵相等<=>对应位置的元素都相等
矩阵的某行(列)乘一个非零的数后矩阵发生改变, 但得到的新矩阵的某些性质得以保留
如: 秩不变, 列(行)向量组的线性相关性不变
绛旓細涓嶇浉绛 涓や釜鐭╅樀鐩哥瓑<=>瀵瑰簲浣嶇疆鐨勫厓绱犻兘鐩哥瓑 鐭╅樀鐨鏌愯(鍒)涔樹竴涓潪闆剁殑鏁板悗鐭╅樀鍙戠敓鏀瑰彉, 浣嗗緱鍒扮殑鏂扮煩闃电殑鏌愪簺鎬ц川寰椾互淇濈暀 濡: 绉╀笉鍙, 鍒(琛)鍚戦噺缁勭殑绾挎х浉鍏虫т笉鍙
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绛旓細1 瀵硅皟涓よ锛2 浠ユ暟k鈮0涔樻煇涓琛岀殑鎵鏈夊厓绱狅紱3 鎶婃煇涓琛屾墍鏈夊厓绱犵殑k鍊嶅姞鍒板彟涓琛屽搴旂殑鍏冪礌涓婂幓銆傝繖涓夌鍙樻崲鍙垵绛夊彉鎹紝鍒濈瓑鍙樻崲鏄竴涓伐鍏凤紝鍏抽敭浣犻渶瑕佸仛浠涔
绛旓細鍙湁涓涓傚悓娴庛婄嚎鎬т唬鏁般嬶紙绗簲鐗堬級绗61椤垫槑纭鏄庯細涓涓煩闃鐨勮鏈绠褰㈢煩闃垫槸鈥滃敮涓纭畾鈥濈殑锛佽鏈绠褰㈢煩闃碉紝鏄寚绾挎т唬鏁颁腑鐨勬煇涓绫荤壒瀹氬舰寮忕殑鐭╅樀銆備笅鍒椾笁绉嶅彉鎹㈢О涓鐭╅樀鐨琛屽垵绛夊彉鎹細锛1锛夊璋冧袱琛岋紱锛2锛変互闈闆舵暟k涔樹互鏌愪竴琛岀殑鎵鏈夊厓绱狅紱锛3锛夋妸鏌愪竴琛屾墍鏈夊厓绱犵殑k鍊嶅姞鍒板彟涓琛屽搴斿厓绱...
绛旓細鐭╅樀鐨勫垵绛夊彉鎹㈡槸鎸囦互涓嬩笁绉嶅彉鎹㈢被鍨嬶細浜ゆ崲鐭╅樀鐨勪袱琛屻佷互涓涓潪闆舵暟k涔樼煩闃电殑鏌愪竴琛鎵鏈夊厓绱犮佹垨鑰呮妸鐭╅樀鐨勬煇涓琛屾墍鏈夊厓绱涔樹互涓涓暟k鍚庡姞鍒板彟涓琛屽搴旂殑鍏冪礌銆傞偅涔堢煩闃靛垵绛夊彉鎹箣鍚庯紝鐭╅樀鐨勭З鏄笉浼氭敼鍙樼殑銆傜煩闃靛彉鎹㈠悗鐨勮鍚戦噺(鍒楀悜閲)鏄師濮嬭鍚戦噺(鍒楀悜閲)绾挎х粍鍚堢殑缁撴灉銆傚鏋滅煩闃电З涓篘锛岀З涓...
绛旓細鐭╅樀鏌愪竴琛屼箻鐩稿悓鐨勯潪闆舵暟k, 鐭╅樀鐨勭З 涓嶅彉 鍘熷洜: 涔樹箣鍓嶄笌涔樹箣鍚庝袱涓煩闃电殑琛屽悜閲忕粍鍙互浜掔浉绾挎ц〃绀 鍗充袱涓悜閲忕粍绛変环 鏁呭畠浠殑绉╃浉鍚 鐭╅樀鐨勭З = 琛岀З = 鍒楃З 鎵浠ョ煩闃电殑绉╀笉鍙.
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