任意m（m<n）个n维向量必线性相关吗？ 刘老师，我完全混乱了，刚才百度了下，当m＞n时，m个n维向量...
\u4e66\u4e0a\u8bf4\u7531 \u63a8\u8bba1\u53ef\u5f97\u4efb\u610fm\u4e2an\u7ef4\u5411\u91cf\u5fc5\u5b9a\u7ebf\u6027\u76f8\u5173(m>n). \u6211\u4e0d\u77e5\u9053\u4ed6\u600e\u4e48\u5f97\u7684\u3002\u6c42\u63a8\u5bfc\u53d6n\u7ef4\u5f97n\u4e2a\u5355\u4f4d\u5411\u91cf
(1,0,...0), (0,1,0...,0), ...(0,0,...,1)
\u663e\u7136\u4efb\u610f\u4e00\u4e2an\u7ef4\u5411\u91cf\u90fd\u53ef\u4ee5\u7531\u4ed6\u4eec\u8868\u8ff0
\u6240\u4ee5m\u4e2a\u5411\u91cf\u7ec4\u6210\u5f97\u5411\u91cf\u90fd\u53ef\u4ee5\u7531\u4ed6\u4eec\u8868\u8ff0
\u6240\u4ee5\u8fd9m\u4e2a\u5411\u91cf\u7ec4\u5f97\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u4e2d\u5411\u91cf\u4e2a\u6570\u4e0d\u53ef\u80fd\u8d85\u8fc7\u8fd9n\u4e2a\u5355\u4f4d\u5411\u91cf\u5f97\u4e2a\u6570
\u6240\u4ee5\u8fd9\u4e2a\u5411\u91cf\u7ec4\u5f97\u5411\u91cf\u4e2a\u6570\u5fc5\u7136\u5927\u4e8e\u5176\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u5f97\u4e2a\u6570\uff0c\u6240\u4ee5\u5fc5\u7136\u7ebf\u6027\u76f8\u5173
\u5bf9\u5440
\u5411\u91cf\u7684\u4e2a\u6570\u5927\u4e8e\u5411\u91cf\u7684\u7ef4\u6570 \u5fc5\u7ebf\u6027\u76f8\u5173!
\u6dfb\u52a0\u5206\u91cf\u662f\u6dfb\u52a0\u7684\u5411\u91cf\u7684\u7ef4\u6570, \u800c\u4e0d\u662f\u6dfb\u52a0\u7684\u5411\u91cf\u7684\u4e2a\u6570.
\u5411\u91cf\u4e2a\u6570\u4e0d\u53d8\u7684\u524d\u63d0\u4e0b, \u5206\u91cf\u8d8a\u591a\u8d8a\u53ef\u80fd\u7ebf\u6027\u65e0\u5173.
绛旓細涓嶆槸锛屽弽浜嗭紝鎶妌缁村悜閲忕湅鎴愬垪鍚戦噺锛m涓猲缁村氨缁勬垚浜唍脳m鐭╅樀锛宮锛渘锛屼笉涓瀹氱嚎鎬х浉鍏筹紝濡傛灉m锛瀗锛岄偅涔堢嚎鎬х浉鍏
绛旓細鈭村～琛ㄤ负 m 1 2 3 AB CD 2 3 2 3 2 3 瀵浠绘剰m锛坢锛0锛夊潎鏈 AB CD = 2 3 锛庣悊鐢憋細灏唝=m 2 锛坢锛0锛変唬鍏= 1 4 x 2 锛屽緱x=卤2m锛屸埓A锛-2m锛宮 2 锛夛紝B锛2m锛宮 2 锛夛紝鈭碅B=4m锛庡皢y=m 2 锛坢锛0锛...
绛旓細瀵浠绘剰瀹炴暟m(m涓嶇瓑浜0锛夊拰n鎭掓垚绔 鍗筹紙|m+n|+|m-n|)/|m|鈮x-1|+|x-2|鎭掓垚绔嬶紝鍗硘1+n/m|+|1-n/m|鈮x-1|+|x-2|鎭掓垚绔嬶紝鍙渶(|1+n/m|+|1-n/m|)min鈮x-1|+|x-2| n/m鐨勫彇鍊艰寖鍥存槸R,褰搉/m鈭圼-1,1]鏃讹紝|1+n/m|+|1-n/m|鍙栧緱鏈灏忓2 鈭磡x-1|+...
绛旓細Cm,n锛漬!/(m!*(n-m)!)涔樻硶鍘熺悊鐨勮瘽锛屽氨鏄紝鍦ㄩ夌涓涓暟鐨勬椂鍊欙紝鏈塶绉嶉夋硶锛屽湪閫夌浜屼釜鏁扮殑鏃跺欙紝鐢变簬绗竴涓暟閫変簡涓涓紝鍓╀簡n-1涓暟锛屾墍浠ユ湁n-1绉嶉夋硶锛屼互姝ょ被鎺紝鍒伴夌m涓暟鐨勬椂鍊欙紝鏈塶-m绉嶉夋硶锛屾妸鎵鏈夌殑涔樿捣鏉ュ氨鏄痭*(n-1)*(n-2)*(n-3)*...*(n-m),浣嗘槸锛岃繖浜...
绛旓細璇佹槑锛氬瓨鍦ㄤ竴涓疄鏁癕 ,鑰屼笖鐐M(M锛-M²)鍦ㄤ簩娆″嚱鏁皔=-½锛坸+1锛²+2涓娿傚皢x = M 浠ｅ叆寮忓瓙涓紝鍥犳 y = f锛圡锛= ½锛圡+1锛²+ 2 = (M ^ 2 + 2M + 5)/ 2 锛屽洜涓 (M ^ 2 + 2M + 5)/ 2 涓嶇瓑鏂 - M ^ 2 .鍥犳鍘熻瘉鏄庝笉鎴愮珛.浠庤岃瘉鏄...
绛旓細M锛坢,-鐨刴鐨勫钩鏂)M鍦3銆4璞￠檺 濡傛灉 -m^2 = -1/2*(m+1)^2+2=-m^2/2-m+3/2 m^2-m+3=0 浣 (m-1/2)^2+5/4>0 鎵浠ワ細m^2-m+3=0鏃犲疄鏁拌В 鎵浠ワ細瀵浠绘剰瀹炴暟m,鐐筂锛坢,-鐨刴鐨勫钩鏂)涓嶅湪鍑芥暟涓
绛旓細璁綪(5cost,3sint)d^2=(m-5cost)^2+9(sint)^2=16(cost)^2-10mcost+m^2+9=16(cost-5m/16)^2+9-(9m^2)/16 鑻5m/16|<=1锛屽嵆-16/5<=m<=16/5, 褰揷ost=5m/16鏃讹紝dmin=(3/4)鈭(16-m^2)鑻5m/16>1锛屽嵆m>16/5, 褰揷ost=1鏃讹紝dmin=|m-5| 鑻5m/16<-1锛屽嵆m<...
绛旓細m(m+5)-(m-3)(m+2)=m²+5m-(m²+2m-3m-6)=m²+5m-m²+m+6 =6m+6 =6(m+1)鐢变簬M涓烘鏁存暟銆傛墍浠6(m+1)鑳借6鏁撮櫎銆
绛旓細鍒嗘瀽锛氱敱浜巑鏄浠绘剰瀹炴暟锛岄偅涔堢洿绾 y锛濓紙3锛峬锛塜锛2m銆灏卞搴旀湁寰堝涓滄枩鐜団濓紝涓嶅悓鏂滅巼瀵瑰簲鐨勭洿绾块兘缁忚繃杩欎釜鈥滃畾鐐光濓紝杩欎釜鈥滃畾鐐光濅笌m 鐨勫彇鍊兼棤鍏炽銆傝瀹氱偣鏄紙X0锛寉0锛夛紝寰 y0锛濓紙3锛峬锛塜0锛2m 鍗炽y0锛3 X0锛m锛2锛峏0锛夌敱浜庡畾鐐逛笌m 鏃犲叧锛屽緱銆X0锛2銆锛岄偅涔堛y0锛6 鍗冲畾鐐规槸...
绛旓細include<stdio.h>#include<math.h>int isprime(int n){ int i;for(i=2;i<=sqrt(n);i++)if(n%i==0)return 0;}int main(){int n,i,j=0;scanf("%d",&n);if(isprime(n))printf("No divisor! %d is a prime number",n);else {i=2;while(i<=n/2){if(n%i==0){if(j)...
