yes
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?