A.B均为可逆矩阵,ACB乘法有意义,为什么r(ACB)=r(C),写出详细步骤和用到...答:A, B 均为可逆矩阵, 则为方阵。设 A(m×m), C(m×n), B(n×n), 则 r(A) = m, r(B) = n,A, B 均为可逆矩阵, 则 ACB 与 C 等价,r(ACB) = r(C)
1.设A.B都是3阶可逆矩阵,且A的行列式等于2,B的行列式等于3/2,则|(AB...答:|(AB)*| = |AB|^2 = (2*3/2)^2 = 3^2 = 9 2. (p1,...,p4) = (a1,...,a4)K 其中 K = 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1 1 --> 1 0 0 1 0 1 0 -1 0 0 1 1 0 0 0 0 因为 a1,a2,a3,a4线性无关 所以 r(p1,...,p4) = r(K) = 3 ...