Assignment:
Q1. Find a vector that, together with vectors [1,1,1], and [1,2,1], forms a basis of R^3.
Q2. Show that the functions (c1 + c2sin^2x + c3cos^2x) form a vector space. Find a basis for it. What is its dimension?
Provide complete and step by step solution for the question and show calculations and use formulas.