Finding a matrix help needed

Let t be a linear transformation.

t:P_3 → R^3

a + bx + cx^2 → (a + c, b, a + b + c).

Find the matrix of s.

The basis of the domain is E = {1, x, x^2}

The basis of the codomain is F = {(1,0,0),(0,1,0),(0,0,1)}

So here is my take on it

S(1,x,x^2) = (a + c, b, a + b + c)

so

s(1) = (1,0,1)

s(x) = (0,1,1)

s(x^2) = (1,0,1)

which gives the matrix below

1 0 1

0 1 0

1 1 1

is that correct the correct method/answer of doing this?

Re: Finding a matrix help needed

Re: Finding a matrix help needed