Generate using code a random integer matrix C of size $4\backslash$times $3$ and a ma$-$ trix A$1$ defined as A$1=$ CT C and workout its characteristic equation. Using any software package, determine the eigenvalues and eigenvec$-$ tors. Deliverables: The matrices C and A$1,$ the computation of the char$-$ acteristic equation, the eigenvalues and eigenvectors as obtained from the package. ii$)$ Write a code in your chosen programming language to implement the Power method and use it to derive the largest eigenvalue $\backslash$lambda $1$ and corre$-$ sponding eigenvector x$1$ of A$1.$ Find $$x$1=$ x$1/$ x$12.$ Compare the values obtained in i$)$ with these values. Deliverables: The handwritten code that implements the Power method, the first $10$ iterates of eigenvalue generated by the algorithm and the final $\backslash$lambda $1$ and $$x$1$ and a comment on the comparison. iii$)$ Write a code to construct matrix A$2=($A$1$x$1$x$1$TA$1).$ Use the Power method code written in ii$)$ and use it to derive the largest eigenvalue $\backslash$lambda $2$ and corresponding eigenvector x$2$ of A$2.$ Find $$x$2=$ x$2/$ x$22.$ Com$-$pare the values obtained in i$)$ with these values. Deliverables: The first $10$ iterates of $\backslash$lambda $2$ and $$x$2$ and a comment on the comparison. iv$)$ Write a code to construct matrix A$3=($A$1$x$1$x$1$TA$1$x$2$xT$2$A$1).$ Use the Power method code written in ii$)$ and use it to derive the largest eigenvalue $\backslash$lambda $3$ and corresponding eigenvector x$3$ of A$3.$ Find $$x$3=$ x$3/$ x$32.$ Compare the values obtained in i$)$ with these values. Deliverables: The first $10$ iterates of $\backslash$lambda $3$ and $$x$3$ and a comment on the comparison. Dont use any inbuilt python libraries