Please give details of the process

In this problem, we consider constructing new kernels by combining existing kernels. Recall that for some function k(x,z) to be a kernel, we need to be able to write it as a dot product of vectors in some high-dimensional feature space defined by : k(x,z)=(x)(z) Mercer's theorem gives a necessary and sufficient condition for a function k to be a kernel function: its corresponding kernel matrix K has to be symmetric and positive semidefinite. Suppose that k1(x,z) and k2(x,z) are two valid kernels. For each of the cases below, state whether k is also a valid kernel. If it is, prove it. If it is not, give a counterexample. You can use either Mercer's theorem, or the definition of a kernel as needed to prove it. (c) [10 points] If k(x,z)=e2xz is a valid kernel, prove that the Gaussian kernel k(x,z)=e22xz22 is also a valid kernel