#3 (20 points) - Working With Cones a.) (15 points) Suppose S is a subset of R n with the property that if x S, then x S for all 0 2. Prove that S is a cone in R n. Hint: Start by considering what happens when 2 3. b.) (5 points) A function f : R n R is said to be homogeneous of non-negative integer degree m if fx m fx for all values of . For example, the function f : R3 R with fx1 , x2 , x3 x1 3x2 x3 4 x1x2 2x3 is homogeneous of degree m 4, since fx1 , x2 , x3 x13x2 x34 x1x22x3 4x1 3x2 x3 4 x1x2 2x3 or fx1 , x2 , x3 4fx1 , x2 , x3. Prove that if the function f : R n R is homogeneous of degree m, then all three sets S x R n|fx 0 , S x R n|fx 0 , S x R n|fx 0 are cones