Assignment:
For each of the following vector spaces, give its dimension and a basis.
(a) The set of all symmetric 4 x 4 matrices,
(b) The subspace of P3 consisting of those polynomials in P3 whose graphs pass through the origin
(c) The set of all vectors in R3 that are orthogonal to v = (1,2,-1)
Provide complete and step by step solution for the question and show calculations and use formulas.