Q3: Choose one of the following two problems: 1 (a) Show that the following equality is true: d² dt2 m A¹h(x(t)) = x(t)¹A₁V²h₂(x(t)) [EXX³h (@(0))] # i=1 (t) + A¹Vh(x(t))ä(t) [15 marks] Where A Rmx1, h: Rnx1 → Rmx1, x R → Rx1 and t E R. The bold notation Vh denotes the Jacobian matrix of h. This calculation is used in week 10 lectures notes (along with some similar versions). (b) Independently investigate non-linear least squares. Provide a concise derivation and con- clude by showing that each iteration of the Gauss-Newton algorithm is equivalent to solving a linear system. [20 marks]

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Q3: Choose one of the following two problems: 1 (a) Show that the following equality is true: d² dt2 m A¹h(x(t)) = x(t)¹A₁V²h₂(x(t)) [EXX³h (@(0))] # i=1 (t) + A¹Vh(x(t))ä(t) [15 marks] Where A Rmx1, h: Rnx1 → Rmx1, x R → Rx1 and t E R. The bold notation Vh denotes the Jacobian matrix of h. This calculation is used in