2. (6 pts) Let K1, K2 be two n x n real positive-definite matrices. Let (x,y); = x"Ky, i = 1,2 be two inner products on R. Let Hill, i = 1, 2 be the induced norms respectively. Assume that a(1),a(2) ER". Consider p(a) = | 219 | + |2 - 22/12 (a) Express p(x) as a quadratic form as x+Kx - 2x+ f +c, and identify K, f.c. Show your steps. (b) Can you conclude that p(x) is positive definite? Justify your answers. 2. (6 pts) Let K1, K2 be two n x n real positive-definite matrices. Let (x,y); = x"Ky, i = 1,2 be two inner products on R. Let Hill, i = 1, 2 be the induced norms respectively. Assume that a(1),a(2) ER". Consider p(a) = | 219 | + |2 - 22/12 (a) Express p(x) as a quadratic form as x+Kx - 2x+ f +c, and identify K, f.c. Show your steps. (b) Can you conclude that p(x) is positive definite? Justify your answers