Assume a polynomial basis that is given by $[1,x,x^2,x^3,\dots,x^{10}]$. Express the polynomial $$f(x) = 1+3x^2-4x^3+x^4+x^6+11x^{7}-5x^8-2x^9+x^{10}$$ as a point in this basis.
(a) Are the elements of the basis linearly independent?
(b) Are the elements of the basis orthogonal?