Given a vector space \\ with dim V = n. along with a spanning set S = (v. ....")} for V with * > n. explain how to find a subset B of S that is a basis for V. Illustrate this procedure in the case V = P (F), with the set of vectors (2r# - r + 3,x3 + 2,3x -1, -13 + 2r, 4r' + 4r +4). Given two ordered bases B and C for the same vector space V, describe how to construct a change-of. basis matrix A having the property that Aizle = [rjc for all vectors r e V. Then, apply this procedure in the case V = F by letting B be the standard ordered basis, letting c -(9) (;) (()) and finding the change of-basis matrix A in this case. Describe the Gram-Schmidt procedure for starting with a linearly independent set { or,..., x } in an in- ner product space V, and constructing an orthogonal set (1, ..., ") with the same span as { or], ..., )- 2 Apply this procedure to the vectors 6 b . ( 8 . ( ) . 1)to give an orthogonal basis for Maxa(F) (with standard inner product)