2. Suppose f : R* R is a quadratic function written in standard form f(x) = xTHx/2 + gTx + d. Assume [ has a minimizer. (a) Let g : R* R be defined by g([z;y]) = f(x + y). Here, [z;y] denotes an arbitrary vector in R?" written in block form as the concatenation of two n-length vectors. Show that g is also a quadratic function by explicitly writing its quadratic, linear, and constant coefficients in terms of H, g, d. Argue that it has a minimizer. (b) Let h : R? R be defined by h(|z;y]) = f(x) + f(y). Argue that h is also a quadratic function by explicitly writing its quadratic, linear, and constant coefficients in terms of H, g,d. Argue that it has a minimizer