Let B={1, x, x², x³} be a basis for P3, and let P={P₁, P2, P3, P4} be the set of polynomials given below: P₁(x) = −2x²-3x+3 P₂(x) = 3x²+x-2 P3(x) = x³-2x²+x-2 P4(x) = −2x³−2x²–2x+1 Find the coordinates of each of these polynomials with respect to the basis B, and use the coordinate vectors to determine whether P is linearly independent, and whether it spans P3. 0 0 0 0 0 0 [P1(x)]B= 0 [P₂(x)]B = 0 0 [P3(x)]B= [P4(x)]B= The set P is linearly independent The set P does not span P3 0 0 0 0

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