True or false T F in a square matrix A nullity A nullityA T

True or false T F: in a square matrix A, nullity (A) = nullity(A). T F: the nullity of an m 8 n matrix is at most m.

Solution

a) True As the dimension of row space and the column space is same, So Nullity of A and its transpose is same

b) True As the number of nonzero solution to AX=0 can not exceed m the number of rows

c) False As the dimension of row space and the column space is same, So Nullity of A and its transpose is same, So nonzero solutions to   AX=0 and A^TX=0 are same

d) False

e) True