Please answer Problem 3(b). If you need solution of Problem 2, please check: https://www.chegg.com/homework-help/questions-and-answers/problem-2-let-x-y-denote-1xn-vectors-elements-x-y-respectively-1n-nxn-matrix-let-f-x-g-x-f-q76856248 ; and Problem 3(a): https://www.chegg.com/homework-help/questions-and-answers/problem-2-let-x-y-denote-1xn-vectors-elements-x-yi-respectively-1n-nxn-matrix-let-f-x-g-x--q80749405?trackid=XbEmilPj

Problem 2 Let x and y denote 1xn vectors (with elements x; and yi, respectively, i=1...n), and A an nxn matrix. Let f(x) and g(x) be functions (f:n+1, g:n>1). Denote the partial derivatives of those functions as vectors of = [df/dx1, 0f/dx2,..., df/dx,]', og = [dg/dx1, dg/dx2,..., dg/dxn)'. Vector and matrix transposes are denoted' and ', respectively. (a) Write the following equations in matrix form: n (i) f(x, X2 7..., X,) = {x,b, n1 11 (ii) g(x, ,x2,..., XY)= Xxxj (b) Demonstrate, for n=3, that the following rules are true: (i) (x'b)'=b'x (ii) (x'A)=Ax (iii) (x'Ay)'=(Ay)'x=y'ATX (iv) Of=b (v) dg=A+AT (vi) Cramer's rule for solving y=x'A for x. Problem 3 (a) Relating to Problem 2, write the Lagrange functions for the following problem: min x'Ax with respect to x subject to x'y=r, where r is a given scalar (number) (b) How is this problem related to optimal portfolio formation in the study of Finance? Problem 2 Let x and y denote 1xn vectors (with elements x; and yi, respectively, i=1...n), and A an nxn matrix. Let f(x) and g(x) be functions (f:n+1, g:n>1). Denote the partial derivatives of those functions as vectors of = [df/dx1, 0f/dx2,..., df/dx,]', og = [dg/dx1, dg/dx2,..., dg/dxn)'. Vector and matrix transposes are denoted' and ', respectively. (a) Write the following equations in matrix form: n (i) f(x, X2 7..., X,) = {x,b, n1 11 (ii) g(x, ,x2,..., XY)= Xxxj (b) Demonstrate, for n=3, that the following rules are true: (i) (x'b)'=b'x (ii) (x'A)=Ax (iii) (x'Ay)'=(Ay)'x=y'ATX (iv) Of=b (v) dg=A+AT (vi) Cramer's rule for solving y=x'A for x. Problem 3 (a) Relating to Problem 2, write the Lagrange functions for the following problem: min x'Ax with respect to x subject to x'y=r, where r is a given scalar (number) (b) How is this problem related to optimal portfolio formation in the study of Finance