98年國立交通大學資訊聯招線性代數線上測驗

1.: Assume A is an m × n matrix with rank r and b is a column vector. Which statements are
true?
(A): (a) If m > r and n = r, then Ax = b must have no solution for some b and exactly one
solution for other b.
(B): (b) If m > r and n > r, then Ax = b has infinitely many solutions for some b and exactly
one solution for other b.
(C): (c) If n = r, then Ax = b has either one solution or none