求解一道线性代数行列式的题，请告诉我过程~谢谢！ 一道线性代数问题，如图，求解这个行列式中的入，要过程，我咋就...
\u6c42\u89e3\u4e00\u9053\u7ebf\u6027\u4ee3\u6570\u9898\uff08\u884c\u5217\u5f0f\uff0c\u6c42\u8be6\u7ec6\u6b65\u9aa4\uff09\u7b54\u6848\u4e3a(b-a)(c-a)(d-a)(c-b)(d-b)(d-c)\uff0c\u8be6\u7ec6\u8fc7\u7a0b\u5982\u56fe\u3002
\u5176\u4e2d\u5229\u7528\u7684\u5230\u4e24\u4e2a\u516c\u5f0f
x²-y²=(x-y)(x+y)
x³-y³=(x-y)(x²+xy+y²)
\u62b1\u6b49 \u56fe\u7247\u6700\u540e\u4e00\u6b65\u7b97\u9519\u4e86\uff0c \u5e94\u8be5\u662fd-c
\u9047\u5230\u9898\u4e2d\u6709\u672a\u77e5\u6570\u4e86\uff0c\u4e00\u822c\u4e0d\u8981\u76f4\u63a5\u5c55\u5f00\uff0c\u91c7\u7528\u964d\u9636\u7684\u65b9\u6cd5\uff0c\u8fd8\u8981\u89c2\u5bdf\u662f\u5426\u6709\u89c4\u5f8b\u53ef\u5bfb\uff0c\u591a\u505a\u51e0\u6b21\u7c7b\u4f3c\u7684\u9898\uff0c\u8fd8\u662f\u5f88\u7b80\u5355\u7684
\u8349\u7a3f\u6bd4\u8f83\u6f66\u8349\uff0c\u8bf7\u89c1\u8c05
1 1 2 3
0 1-x^2 0 0
2 3 1 5
0 0 0 -1-x^2
因此该行列式等于
(1-x^2)(-1-x^2)|1 1|
|2 1|
=(1-x^2)(-1-x^2)(1-2)
故有2个实根，分别为1，－1。
绛旓細1 1 2 3 0 1-x^2 0 0 2 3 1 5 0 0 0 -1-x^2 鍥犳璇琛屽垪寮绛変簬 (1-x^2)(-1-x^2)|1 1| |2 1| =(1-x^2)(-1-x^2)(1-2)鏁呮湁2涓疄鏍癸紝鍒嗗埆涓1锛岋紞1銆
绛旓細绛旀涓(b-a)(c-a)(d-a)(c-b)(d-b)(d-c)锛岃缁嗚繃绋嬪鍥俱傚叾涓埄鐢ㄧ殑鍒颁袱涓叕寮 x²-y²=(x-y)(x+y)x³-y³=(x-y)(x²+xy+y²)鎶辨瓑 鍥剧墖鏈鍚庝竴姝ョ畻閿欎簡锛 搴旇鏄痙-c
绛旓細I(n-1)=XI(n-2)+An-1 .I2=XI1+A2 鑰 I1=X+A1 浠ヤ笂鍚勯」Ii涔樹互X^(n-i),鐒跺悗鍔犺捣鏉ュ緱,In =X^(n-1)I1+X^(n-2)A2+.XAn-1+An =X^n+X^(n-1)A1+X^(n-2)A2...+XAn-1+An,2,涓閬鍏充簬绾挎т唬鏁拌鍒楀紡鐨勯 X (-1) 0 ...0 0 0 X (-1)...0 0 .0 0 0 .....
绛旓細濡傛灉鍖栫畝鏉ヨВ锛宺3-r1/s= s -1 0 0 s+4 -3 0 1+1/s s+2 鎸夌涓鍒楀睍寮 = s(s²+6s+8 +3+3/s)鍗冲緱鍒琛屽垪寮鍊=s³ +6s²+11s +3
绛旓細鍙渶璇佹槑杩欎釜绯绘暟鐭╅樀A鐨琛屽垪寮|A|涓嶄负0锛屽嵆鍙緱鐭ユ柟绋嬬粍鏈夊敮涓瑙ｏ細A= a b c d b -a d -c c -d -a b d c -b -a 鏄剧劧绯绘暟鐭╅樀A鏄弽瀵圭О鐭╅樀(A^T=-A)锛屽垯 |A|^2=|A^2|=|A(-A^T)|=(-1)^4|AA^T|=|AA^T|=|(a^2+b^2+c^2+d^2)I|=(a^2+b^2+c^2+d^...
绛旓細杩欑棰樼洰绉颁负婊戞褰琛屽垪寮忥紝鏈変竴绉嶅吀鍨嬬殑瑙ｉ鏂规硶銆傚氨鏄粠绗竴鍒楀紑濮嬶紝渚濇鍚戝悗锛屾秷鍘讳富瀵硅绾夸笂鏂圭殑鍏冪礌锛屽寲涓轰笁瑙掑舰琛屽垪寮忋傝В绛斿涓 棣栧厛鍋囪x涓嶄负0锛屽皢绗竴鍒楃殑1/x鍔犲埌绗簩鍒楋紝鍐嶅皢绗簩鍒楃殑1/x鍔犲埌绗笁鍒楋紝鏈鍚庡皢绗笁鍒楃殑1/x鍔犲埌绗洓鍒楋紝鍒欏寲涓轰簡涓嬩笁瑙掑舰琛屽垪寮忥紝鍏朵富瀵硅绾跨嚎涓婂厓绱犵殑...
绛旓細绗竴琛屼箻浠-1鍔犲埌涓嬮潰鍚勮锛岀k鍒椾箻浠1/ak鍔犲埌绗竴鍒楋紝k=2,3,...,n锛岃鍒楀紡鍖栨垚涓婁笁瑙掑舰锛岀粨鏋滄槸(1+鈭1/ak)鈭廰k锛宬浠1鍒皀銆
绛旓細绗2琛屾彁鍑哄洜瀛2锛岀3琛屾彁鍑哄洜瀛2锛...锛岀n琛屾彁鍑哄洜瀛恘锛屽氨鍖栨垚浜嗚寖寰疯挋琛屽垪寮忥紝鍙互濂楃敤鍏紡璁＄畻锛堢涓琛岀湅鎴 1 1 1^2 ... 1^(n-1)锛夈
绛旓細琛屽垪寮忕瓑浜庡畠鐨勪换鎰忎竴琛(鍒)鐨勫悇鍏冪礌涓庡叾瀵瑰簲鐨浠ｆ暟浣欏瓙寮忎箻绉箣鍜 宸茬煡琛屽垪寮忕殑鍏冪礌aij鐨勪綑瀛愬紡涓篗ij,鍒欏叾浠ｆ暟浣欏瓙寮忎负(-1)鈭(i+j)Mij 杩欓噷鍙栫涓鍒楁墍鏈夊厓绱狅紝鍏朵綑瀛愬紡涓轰笂涓夎琛屽垪寮忔垨涓轰笅涓夎琛屽垪寮
绛旓細| 2 0 1 -1| |16 0 -2 7| 鎸夌 2 鍒楀睍寮锛屽緱 A = (-1)|-8 4 -6| | 2 1 -1| |16 -2 7| 绗 2 鍒 -2 鍊嶏紝 1 鍊 鍒嗗埆鍔犲埌绗 1锛 3 鍒楋紝寰 A = (-1)|-16 4 -2| | 0 1 0| |20 -2 5| 鎸夌 ...
