设α=(1,-1,2)T,β=(2,1,1)T,A=αβT,则An=________.

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问题 设α=(1,-1,2)T,β=(2,1,1)T,A=αβT,则An=________.

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答案3n-1[*]

解析 βTα=3,A2=αβT·αβT=3αβT=3A,则An=3n-1A=3n-1
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