已知三维矩阵A与三维列向量x满足...,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B,使AP=PB已知三维矩阵A和三维列向量X满足:XA^3=3AX-2XA^2,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求
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![已知三维矩阵A与三维列向量x满足...,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B,使AP=PB已知三维矩阵A和三维列向量X满足:XA^3=3AX-2XA^2,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求](/uploads/image/z/2653772-68-2.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%89%E7%BB%B4%E7%9F%A9%E9%98%B5A%E4%B8%8E%E4%B8%89%E7%BB%B4%E5%88%97%E5%90%91%E9%87%8Fx%E6%BB%A1%E8%B6%B3...%2C%E4%B8%94%E5%90%91%E9%87%8F%E7%BB%84X%2CAX%2CA%5E2X%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%2C%E8%AE%B0P%3D%EF%BC%88X%2CAX%2CA%5E2X%EF%BC%89%2C%E6%B1%82%E4%B8%89%E9%98%B6%E7%9F%A9%E9%98%B5B%2C%E4%BD%BFAP%3DPB%E5%B7%B2%E7%9F%A5%E4%B8%89%E7%BB%B4%E7%9F%A9%E9%98%B5A%E5%92%8C%E4%B8%89%E7%BB%B4%E5%88%97%E5%90%91%E9%87%8FX%E6%BB%A1%E8%B6%B3%EF%BC%9AXA%5E3%3D3AX-2XA%5E2%2C%E4%B8%94%E5%90%91%E9%87%8F%E7%BB%84X%2CAX%2CA%5E2X%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%2C%E8%AE%B0P%3D%EF%BC%88X%2CAX%2CA%5E2X%EF%BC%89%2C%E6%B1%82)
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已知三维矩阵A与三维列向量x满足...,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B,使AP=PB已知三维矩阵A和三维列向量X满足:XA^3=3AX-2XA^2,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求
已知三维矩阵A与三维列向量x满足...,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B,使AP=PB
已知三维矩阵A和三维列向量X满足:XA^3=3AX-2XA^2,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B使AP=PB
已知三维矩阵A与三维列向量x满足...,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求三阶矩阵B,使AP=PB已知三维矩阵A和三维列向量X满足:XA^3=3AX-2XA^2,且向量组X,AX,A^2X线性无关,记P=(X,AX,A^2X),求
是 A^3X=3AX-2A^2X
(1) AP = A(X,AX,A^2X)
= (AX,A^2X,A^3X)
= (AX,A^2X,3AX-2A^2X)
= (X,AX,A^2X)B = PB.
其中 B =
0 0 0
1 0 3
0 1 -2