Question

n阶方阵A,B满足矩阵方程AB=0,则秩R(A)+R(B)____n（≤,≥,＜,＞,＝）

Answer 1

答案是 ≤

假设 A = O ,B = O

显然满足题意 AB = O

此时 R(A) + R(B) = 0 < n

假设 A = E,B = O

显然也满足题意 AB = O

此时 R(A)+R(B) = n

综上 R(A)+R(B) ≤ n