线性代数提高线性代数随机推荐教材习题蒲和平非数习题解答习题 9.1行列式与矩阵繁琐不看本题本题讨论已掌握查看解析收入错题#15937设 A,BA,BA,B 为 nnn 阶矩阵，证明下列等式:(1) rank(A−ABA)=rank(A)+rank(I−BA)−n\operatorname{rank}\left( {A - {ABA}}\right) = \operatorname{rank}\left( A\right) + \operatorname{rank}\left( {I - {BA}}\right) - nrank(A−ABA)=rank(A)+rank(I−BA)−n(2) rank(A+B−ACB)=rank(A+B−BCA)\operatorname{rank}\left( {A + B - {ACB}}\right) = \operatorname{rank}\left( {A + B - {BCA}}\right)rank(A+B−ACB)=rank(A+B−BCA) .