Which of the following lies in the kernel of the linear tran

Which of the following lies in the kernel of the linear transformation T defined by T(x, y, z) = (x, y, 0) (a) (0, 2, 3) (b) (2, 0, 3) (c) (3, 0, 0) (d) 0, 0, 2 (e) (2, 1, 0) Suppose T: R^n rightarrow R^m, is defined by T(X) = AX and rank (A) = r. Then nullity (T) is (a) r - n (b) n + r (c) n - r (d) 0 (e) -r

Solution

18.

kernel of the linear transformation T defined by T (x,y,z) = (x,y,0)

the kernel consists of all the vectors lying on the z-axis.

ker(T) = (0,0,z) therefore

option d (0,0,2)