Answer all the questions

Q$1)$ Power Method and Associated problems

$(2$ marks$)$

i$)$ Generate using code a random integer matrix $C$ of size $43$ and a matrix $A_1$ defined as $A_1=C^{T}C$ and workout its characteristic equation. Using any software package, determine the eigenvalues and eigenvectors.

Deliverables: The matrices $C$ and $A_1,$ the computation of the characteristic equation, the eigenvalues and eigenvectors as obtained from the package.

$(0\mathrm{.}5$ marks$)$