Practice questions Linear Algebra/ Advanced Math Let v. = (5,2,6,4), v2 = (12,3,12,6), and v3 = (2a + 3.8a + 3, Ba + 6,2a 6), where a is some unknown real number. Let V = span IV1. v2, v3}. (3) Transform {V|,V2.V3} into an orthonormal basis for V by applying the Gram-Schmidt Process. Orthononnal bases obtained using a method different from the Gram-Schmidt Process will not be accepted. Hint: your solution will depend on the value of 0. Also, all entries in the solution are rational numbers. (b) What are the possible values for dim(V)? (e) Let T be the orthonormal basis for V found in Part (a). In the case when dim(V) = 3, nd the transition matrix from .S' to T. where S = {v.,vz, v3}. Hint: all entries in the solution are integers or integer multiples of 0. (cl) Find a least squares solution to 5-12 5 4 2 -311x_ 7 612 3 "9' 4 64 5