6. Consider the polynomial kernel function K (R2, R) R defined by K(x, y) = (xTy + 1). The associated feature map and the feature space H are given explicitly as in the following 0 : x = (x1, x2) (x) = (2x1, 2x2, x1, x2, 2x1x2, 1) = R6 := H. This feature map takes the data from a two-dimensional to a six-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) = ((x), (y)), and prove K is symmetric positive semi-definite (SPSD).