QUESTION 1 Let fa, fb, fc P2(R) denote the Lagrange polynomials associated with the distinct real numbers a, b, c respectively. Let V = span{ fa, fa + fo} and W = span{fa + fo + fc}, let T : P2 (R) + P2(R) be the projection on V along W, and let g P2(R). (1.1) Show that B = {fa, fa + fo, fa + fo + fc} is linearly independent. (5) (1.2) Show that P2(R)= V W. (2) (1.3) Find a formula for T(g) expressed as a linear combination of {fa, fb, fc}. (8) [15]