6. Consider the polynomial kernel function K : (R', R?) + R defined by K(x, y) = (aTy + 1)2. The associated feature map $ and the feature space H are given explicitly as in the following 9:x= (21, 12) + 6(x) = (x1, 23, V2:12, 1) ER4 := H. This feature map takes the data from a two-dimensional to a four-dimensional space in a way that linear relations in the feature space correspond to quadratic relations in the input space. Prove that indeed o and H satisfies K(x, y) = (9(x), (y)), and prove k is symmetric positive semi-definite (SPSD)