試題詳解

ㆍLet A be an m✕  n real-valued matrix of rank r. and b be an m✕ 1 real-valued vector. Which of the following statement is/are true?
(A). The equation Ax = b has non-trivial solutions if n ＞ r ＞ 1 and b is all-zero.
(B). The equation Ax = b has solutions if b belongs to the column space of A.
(C). The equation Ax = b has only one solution when r = m.
(D). The dimension of the nullspace of A is O if the dimension of the row space of A is r.
(E). None of the above is true.