Problem:
Linear Algebra: Matrix of Transformation
Are the following examples linear transformations from p3 to p4? If yes, compute the matrix of transformation in the standard basis of P3 {1,x,x^2} and P4 {1,x,x^2,x^3}.
(a) L(p(x))=x^3*p''(x)+x^2p'(x)-x*p(x)
(b) L(p(x))=x^2*p''(x)+p(x)p''(x)
(c) L(p(x))=x^3*p(1)+x*p(0)