2. (SCPMK 4, 30 points) The formula = ujV1 + 2uzV2 + U3V3 defines an inner product on R3, where u = (u1, U2, U3 ) and v = (V1, V2, V3 ). Consider the basis S = {w1, W2, W3), where w1 = (1,1,1), W2 = (1,1,0), and W3 = (1,0,0). a) Determine if S is an orthonormal basis relative to the stated inner product. b) If S is not orthonormal, build an orthonormal basis S' using the Gram- Schmidt process and normalization.4. (SCPMK 5, 20 points) Let T: R3 > R2 be a linear transformation and let T=m M a. Knowing that {(1, 1, 1), (1, 1,0), (0, 1, 1)} forms a basis for R3, determine the explicit formula for T, that is, T (X1, X2, X3), for any vector (X1, X2, X3) in R3. 2 3 D 1 c. Determine bases for ker(T) and R(T) and specify their dimensions. 3])=<_11 b. use the formula derived in part a to nd t>