試題詳解

複選題
1. Consider a 3x3 matrix A with non-zero elements. Assume A^TAx=0 has non-trivial solutions with two of them being x=[1,1,0]^T and [1,0,0]^T. Which of the following statements are true for b,y ∈ R³?
(A) Ay =b must have no solution for some b and exactly one solution for other b.
(B) A^Ty=[0,0,5]^T must have at least one exact solution.
(C) The least-squares approximation error for the system A^Ty =[0,2,2]^T is 4.
(D) Rank of A =2.
(E) A must have zero rows.