线性代数，求问！！！！！！急 线性代数求！！！
\u7ebf\u6027\u4ee3\u6570\u77e9\u9635\u7684\u95ee\u9898\u554a\uff01\uff01\uff01\uff01\uff01\uff01\uff01\u6ce8\u610f\uff1a\u4e00\u4e2a\u884c\u5217\u5f0f\u7684\u503c\u662f\u4e00\u4e2a\u552f\u4e00\u786e\u5b9a\u7684\u503c\uff0c\u4e0d\u53ef\u80fd\u540c\u65f6\u5bf9\u4e8e\u4e24\u4e2a\u4e0d\u540c\u7684\u503c\u3002
\u5728\u8be5\u9898\u76ee\u7684\u6761\u4ef6\u4e0b
|A+E|\u53ea\u80fd\u662f\u7b49\u4e8e0\uff0c\u90a3\u4e48\u5c31\u4e0d\u53ef\u80fd\u7b49\u4e8e-1.
\u8fd9\u662f\u7531\u4e8e\u4f60\u7684\u8bc1\u660e\u8fc7\u7a0b\u672c\u8eab\u6709\u95ee\u9898\u3002
\u6b63\u786e\u7684\u8bc1\u660e\u53ea\u8981\u5c06\u4f60\u8bc1\u660e\u7684\u524d\u534a\u90e8\u5206\u518d\u9002\u5f53\u53d8\u5f62\u5c31\u53ef\u4ee5\u4e86\u3002\u8bc1\u660e\u5982\u4e0b
\u8bc1\u660e\uff1a\u56e0\u4e3aAAT=E,\u4e14|A|<0,\u6240\u4ee5|A|=-1
\u4ece\u800c |A+E|=|A+AAT|=|A||E+AT|=|A||\uff08E+A\uff09T|=|A||A+E|=-|A+E|
\u6240\u4ee5 |A+E|=-|A+E|
\u6545|A+E|=0
1\uff0c\u63d0\u53d6\u7cfb\u6570\u77e9\u9635
2\uff0c\u5bf9\u7cfb\u6570\u77e9\u9635\u521d\u7b49\u884c\u53d8\u6362\u5316\u6210\u6700\u7b80\u9636\u68af\u5f62
3\uff0c\u5199\u51fa\u7b49\u4ef7\u5173\u7cfb\u6216\u8005\u901a\u89e3\u7b49
\u901a\u89e3\u4e3a\uff1a
证明：A为实反对称矩阵，因此A的特征值必为零或纯虚数即实部为零。则E+A的特征值非零，从而E+A可逆。
注：设a+ib是A的特征值，X+iY是相应的特征向量，则
(X-iY)'A(X+iY)=(a+ib)(X-iY)'(X+iY)
两边同取共轭转置，得
(X-iY)' A' (X+iY)=(a-ib)(X-iY)'(X+iY)
而A实反对称，因此上式又等于
(a-ib)(X-iY)'(X+iY)=(X-iY)' A' (X+iY)=-(X-iY)'A(X+iY)=-(a+ib)(X-iY)'(X+iY)
注意到(X-iY)'(X+iY)非零，从而a=0.
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绛旓細(1)鑻鏄疉鐨勭壒寰佸硷紝鍒橞鐨勭壒寰佸兼槸k^3+2k^2-1锛屾墍浠鐨勭壒寰佸间负0,15,44 (2) B鐨勮鍒楀紡涓0锛孉-4E鐨勭壒寰佸间负-4,11,40鎵浠-4E鐨勮鍒楀紡涓-4*11*40=-1760
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绛旓細澧炲箍鐭╅樀 (A, b) = [2 1 -1 1 1][1 -1 1 1 2][7 2 -2 4 a][7 -1 1 5 8]鍒濈瓑琛屽彉鎹负 [1 -1 1 1 2][0 3 -3 -1 -3][0 9 -9 -3 a-14][0 6 ...
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绛旓細P = (p1 p2 p3)D = 1 0 0 0 0 0 0 0 -1 鍥犱负 P^(-1)*A*P = D 鎵浠 A = P*D*P^(-1) = (涓嬪浘)
