Suppose A is a 3x4 matrix with rankA 3 Which of the followi

Suppose A is a 3x4 matrix with rank(A) = 3. Which of the following are true?
(i) The rank of AT is 2.
(ii) The nullity of AT is 1.
(iii) There exists a nonzero 4x1 matrix B such that AB = 0.
(iv) The rows of A are linearly dependent.
(v) The columns of A are linearly dependent.
A. (i) only
B. (ii) only
C. (v) only
D. (iii) and (iv)
E. (iii) and (v)

Solution

Answer: The correct answer is E as only (iii) and (v) are true.