Problem 1 (Projection). 1. Let v = (6, 3, -2), w = (9, -4, -1). Find proj,(w) and projw(v). 2. Letv = (-3,5,7). Find some w E R3 such that proj, (w) = (9, -15, -21). Problem 2 (Projection onto Coordinates). 1. Let x = (21, . .. ,In). Recall that e1 = (1, 0, . . . , 0) , e2 = (0, 1, . . . ,0) , en = (0, . . . ,0, 1) . Compute proje, (x) for all i = 1, . .. , n. Find the relationship between x and proje, (x) for i = 1, . . . , n. 2. Compute el . el, . .. , en . en. Also compute er . e; for i # j. Convince yourself that ei . e; only depend on whether i = j or not