Problem 2 Suppose that A is a 9 6 matrix and nullityA 4 a

Problem 2. Suppose that A is a 9 × 6 matrix and nullity(A) = 4. (a) Find rank(A).

Solution

given that matrix A has order 9x6 and nullity of A = 4.

(a) Since, we know that

rank A + nullity A = number of columns of A

rank A + 4 = 6

rank A = 6 - 4 = 2

(b) since rank A = rank A^T

So, rank  A^T = 2

(c) Since

rank A^T + nullity A^T = number of columns of A^T

2 +  nullity A^T = 9

nullity A^T = 9 - 2 = 7