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\fExercise 3. Find the coordinate vector [x]3 of 3: relative to the basis B = {b1,b2}. b1: [3] 1'2 = [I'll x= Lil Exercise 4. The set as = {1 t2, 2t +t2, 1 + t 132} is a basis for P2. Find [p]3, the coordinate vector of p(t) = 1 7t + 2t2 relative to 55. Hint: You are trying to nd cl, (12, and 03, so that c1(1 t2) + c2(2t + :2) + c3(1 + t t2) = 1 775 + 21:2. Reordering terms gives: (cl + C3) + (202 + C3)t + (31 + c; (:3)t2 = 1 77: + 2t2. Noting that the coeicients on the left and right hand side have to match, use this equation to come up with a system of 3 linear equations in the unknowns cl, 02, and 03. Solving the system will give you [p]55