Q5) Consider the following function f ( x , yz ) = ajx2 + azy' + azz + atxy + agxz + agyz + axx + agy + doz + @10. Suppose that f(x,y,z) has a minimum. a) Describe how the minimum of f(x,y,z) can be found by solving a system of linear equations. (2 marks) b) What are the sufficient conditions for finding the solution of the system of linear equations in Part a using the Gauss-Seidel method? (2 marks) c) Consider a general function g(x,y) which may not be quadratic, but has a minimum. How can the minimum of g(x,y) be found iteratively, by solving a system of linear equations at each iteration? Mention all the details of your solution. (12 marks) Hint: The Taylor expansion of g(x,y) around (xo,yo) can be written as g(x,y) = g(xoyo) + (x -xo)- Bx -+ (y -vo) dy + ; (v - vo)? +(x - xo) (y - yo)- Exdy + (x - x0)2 (y - yo) axdy +i(x - x)(y - y)20 s (xox) dxdyz -+... d) What are the sufficient conditions for finding the solution of the system of linear equations in Part c using the Gauss-Seidel method? (4 marks)