Let U = {v1, v2} where v1 = (1, 1,-2) and v2 = (2, 0, 3) as vectors of R3. Answer the following questions including of derivations when is appropriate. Using the Set Theory notation, write the span U and determine whether v3 = (1, 2,-1) span U. Compute w = proj w v3, if W, (make the proper derivation) Indicate what W is geometrically, and find its equation. Compute W1 and describe it geometrically. Using the Gram Schmidt process, find an orthonormal set from T = {v1, v2, v3}. Show details of derivation. If S is the orthonormal set found in 5, find the transition matrix from S to T.
