设n阶矩阵A的各行元素之和均等于2，且A²+kA+6E=0，其中E是n阶单位矩阵，则参数k等于多少？
\u8bben \u9636\u77e9\u9635A \u7684\u884c\u5217\u5f0f\u7b49\u4e8eD \uff0c\u5219(KA)* =\u77e5\u8bc6\u70b9: |A*| = |A|^(n-1)
\u89e3:
|(kA)*| = |kA|^(n-1) = (k^n|A|)^(n-1) = k^n(n-1) |A|^(n-1) = k^n(n-1) D^(n-1)
\u6ee1\u610f\u8bf7\u91c7\u7eb3^_^
\u8bc1\u660e: \u56e0\u4e3ar(A)=1
\u6240\u4ee5 A \u6709\u4e00\u4e2a\u975e\u96f6\u5217\u5411\u91cf\u03b1, \u4e14\u5176\u4f59\u5217\u5411\u91cf\u90fd\u662f\u03b1\u7684\u500d\u6570
(\u4e8b\u5b9e\u4e0a,\u03b1\u662fA\u7684\u5217\u5411\u91cf\u7ec4\u7684\u4e00\u4e2a\u6781\u5927\u65e0\u5173\u7ec4)
\u8bb0\u03b1=(a1,a2,...,an)'
\u5219 A = (k1\u03b1,k2\u03b1,...,kn\u03b1) \u67d0\u4e2aki=1.
= \u03b1(k1,k2,...,kn)
\u8bb0 \u03b2 = (k1,k2,...,kn)'
\u5219 A = \u03b1\u03b2'.
\u6240\u4ee5 A^2 = (\u03b1\u03b2')(\u03b1\u03b2')=\u03b1(\u03b2'\u03b1)\u03b2'=(\u03b2'\u03b1)\u03b1\u03b2'=(\u03b2'\u03b1)A.
\u4ee4 k = \u03b2'\u03b1
\u5219 A^2=kA.
\u6ce8: \u03b2'\u03b1 \u662f\u4e24\u4e2a\u5411\u91cf\u7684\u5185\u79ef, \u662f\u4e00\u4e2a\u6570.
由已知, 2^2 +2k+6 = 0
所以 k = -5
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