Solve the following problems, showing any necessary work. Let , S = , and W be the subspace spanned by S. Note that S is a linearly dependent set of vectors. Find a nontrivial linear combination of that adds up to 0. Find a basis for W, and the dimension of W. Let B be the ordered basis , C the ordered basis , and Find the coordinates of with respect to B. Find the change-of-basis matrix from C to B.
