求一道线代证明题谢谢~已知A为三阶方阵且有三个不同的特征值λ1,λ2,λ3,对应的特征向量依次为α1,α2,α3,令β=α1+α2+α3,证明:向量组β,Aβ,A^2β线性无关
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![求一道线代证明题谢谢~已知A为三阶方阵且有三个不同的特征值λ1,λ2,λ3,对应的特征向量依次为α1,α2,α3,令β=α1+α2+α3,证明:向量组β,Aβ,A^2β线性无关](/uploads/image/z/4327744-40-4.jpg?t=%E6%B1%82%E4%B8%80%E9%81%93%E7%BA%BF%E4%BB%A3%E8%AF%81%E6%98%8E%E9%A2%98%E8%B0%A2%E8%B0%A2%7E%E5%B7%B2%E7%9F%A5A%E4%B8%BA%E4%B8%89%E9%98%B6%E6%96%B9%E9%98%B5%E4%B8%94%E6%9C%89%E4%B8%89%E4%B8%AA%E4%B8%8D%E5%90%8C%E7%9A%84%E7%89%B9%E5%BE%81%E5%80%BC%CE%BB1%2C%CE%BB2%2C%CE%BB3%2C%E5%AF%B9%E5%BA%94%E7%9A%84%E7%89%B9%E5%BE%81%E5%90%91%E9%87%8F%E4%BE%9D%E6%AC%A1%E4%B8%BA%CE%B11%2C%CE%B12%2C%CE%B13%2C%E4%BB%A4%CE%B2%3D%CE%B11%2B%CE%B12%2B%CE%B13%2C%E8%AF%81%E6%98%8E%3A%E5%90%91%E9%87%8F%E7%BB%84%CE%B2%2CA%CE%B2%2CA%5E2%CE%B2%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3)
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