In: Advanced Math
Consider the following vectors {1 + x + x^2, 1 - x^2, x + 2, 1 - x}. a) Test or refute if the vector set is linearly independent? b) Construct a linearly independent set of dimension 2, describe the shape of the generated space. c) Construct a linearly independent set of dimension 3, describe the shape of the generated space. d) For the base you chose in part c), find a linear combination for p (x) = 3 + 11x + 8x^3