1) Suppose D: \mathbb{R}^3[x] \to \mathbb{R}^2[x] is linear and you know what it does to vectors in
the basis B = \{1, 1 - x, x - x^3, x^2 + 2\}:
D(1) = 0
D(1 - x) = 1 + x
D(x - x^3) = 1 - 3x
D(x^2 + 2) = x - x^2
a) Find D(2x^3 - 3x^2 + x - 4). (24points)
b) For given basis B' = \{x, 1, x + x^2, x^3\} find M_B^{B'}(id). (24 points)