1. For a n-vector x, with n = 2m – 1 odd, we define the median of x as the scalar value x_a such that exactly n of the values in x are ≤ x_a and n are ≥ x_a (i.e., x_a leaves half of the values in x to its left, and half to its right). Now consider the function f : Rⁿ → R, with values Express f as a scalar product, that is, find a ∈ Rⁿ such that f(x) = a^Tx for every x. Find a basis for the set of points x such that f (x) = 0.

2. For a ∈ R², we consider the “power law” function f : R² ₊₊ → R, with values f (x) = x₁^α1 x₂^a2. Justify the statement: “the coefficients α_i provide the ratio between the relative error in f to a relative error in x_i”.

n f(x) = x - | =1 Xa