设A={3 0 1 1 1 0 0 1 4 },且满足AB=A+2B,求B的矩阵
问题描述:
设A={3 0 1 1 1 0 0 1 4 },且满足AB=A+2B,求B的矩阵
答
因为 AB=A+2B所以 (A-2E)B=A(A-E,A) =1 0 1 3 0 11 -1 0 1 1 00 1 2 0 1 4r2-r11 0 1 3 0 10 -1 -1 -2 1 -10 1 2 0 1 4r3+r2,r2*(-1)1 0 1 3 0 10 1 1 2 -1 10 0 1 -2 2 3r1-r3,r2-r31 0 0 5 -2 -20 1 0 4 -3 -20 0 ...