3. (3 points each) In each of the following, one is given two vector spaces V and W and a

transformation T: V→ W. Determine if T is linear.

(a) V = W = M2x2 (R), T is defined by

(b) V = R₂[X], W = R, T is defined by

T(A) = AT.

1

T(a+bX+cX²) = a +b+c+1.

(c) V = R², W = M₂x2 (R), T is defined by

T(x) = x¹x.