这是一个英国的R统计assignment代写

Question 1

a) Cleary showing your calculations, work out by hand the lower triangular matrix L in
Cholesky’s decomposition of the matrix,

b) Next, write an R function to produce the lower triangular matrix L in Cholesky’s decom
position of an arbitrary n × n positive definite, symmetric matrix.

Use your function to check your answer in part (a).

Question 2

a) Cleary showing your calculations, work out by hand the singular values and the matrices

in the singular value decomposition of

b) Write R code to check your answer in part (a) and comment on any differences between
your answer in part (a) and the R output.

Question 3

Consider a system with differential equation given by

a) Determine the transient and steady state solutions for y, and hence find the particular
solution if

b) Next, use R to obtain a numerical solution of the above differential equation and plot
graphs showing the theoretical and numerical solutions for t in the interval (0; 5).