Assume that A is a 2 times 3 matrix Prove or disprove the fo

Assume that A is a 2 times 3 matrix. Prove or disprove the following statements. (a) dim Row (A) > dim Col (A) (b) rank (4)

Solution

we have rank of A + nullity of A = n , where n is number of columns of a matrix from this we infer that since matrix A is a 2x3 matrix , n=3 . a) number of rows is less than number of columns

b) rank of A cannot be less tham nullity

c)dim null A cannot be greater than 1

d)false does not hold good