Question

Let T : P1 → P2 be defined by
T(a+bx) = b+ax+(a−b)x^2.
Check that T is a linear transformation. Find the matrix of the transformation with
respect to the ordered bases B1 = {1,x} and B2 = {x^2,x^2+x,x^2+x+1}. Find the
kernel of T . Further check that the range of T is
{a+bx+cx^2 ∈ P2 | a+c = b}.