1. This question explores some generalizations of the standard Eulcidean norm and inner product. You will need to use the definitions of norms and inner products that we covered in the first week of class. These generalizations are particularly useful if you have data at unevenly sampled points (e.g. in space), and need to weight your data to account for this. (a) Consider the function f(x): C" R defined by f(x) = = n clajl, where x = (x1, x2, xm), and each c; > 0. Show that f can be used a norm. Why do we need the condition that c; > 0?