Vector space

Let Real[x]_(=<2) be the vector space of polynomials of degree at most 2 over Real. Let e_1, e_2, e_3 and e'_1, e'_2, e'_3 be te bases 1, x, x^2 and 1, (1-x), (1+x)^2 of Real[x]_(=<2).

i) Write down the basis change matrices from basis e'_i to basis e_i and from basis e_i to basis e'_i.
(Note: Use the definition saying the basis change matrix from basis e'_i to basis e_i has columns that represent e'_i in term of the e_i.)

ii) Use (i) to write the polynomial 3 - 4x - 2x^2 as a linear combination of e'_1, e'_2, e'_3, and then check your answer by direct calculation.