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).
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.
Consider a system with differential equation given by
a) Determine the transient and steady state solutions for y, and hence find the particular
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).