For eath linear transformation below find I he kernel nullit

For eath linear transformation below, find I he kernel. nullity, range, rank, ami deteimiue if T is 1-1 and/or onto. T: P^2 rightarrow P2 given by T(p(x)) = d/dx[p(x)]. T: M2,2 rightarrow M2,2 given by T(A) = A^T. T: R^3 rightarrow R^4 given by T(x, y, z) rightarrow (x, y, z,t

Solution

(a)

Kernel of T is {c(x)}, where c(x) is a constant polynomial.

(b)

Ker T = {O}, where O is the null matrix.

(c)

Ker T = {(0,0,0)}

(d)

Ker T = {(0,0,0)}