0 0 0 0

1.W.4 We'll work inside the vector space of polynomials in degree < 2, which is denoted P<2. Let P1 = 1, p2 = x + 2, and p3 = (x + 2)². Leť's think about Span{p1, P2, P3}. a) What polynomial is 3p1 + 2p2 – P3? b) I claim that a = a¡P1 + a2P2 + azp3 for some coefficients a1, a2, az in R. Find a1, a2, az. Hint: az = 0. c) I claim that a? = bịPi + b2p2 + b3p3 for some coefficients b1, b2, bz in R. Find b1, b2, bz. Hint: This problem isn't quite so cut and dry. Try to find three equations, one for each coefficient in the polynomial, and solve them for b1, b2, b3.

Suppose given vector space V = P_3, given four polynomials in image. Can we use them as basis set for V? If so, find the coordinates under the basis set for the given equation in the image

Which of the sets form a basis for R?? Explain your reasoning (if yes, why; if not, why).