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Generate using code a random integer matrix C of size 4 times 3 and a ma - trix A 1 defined as A 1
Generate using code a random integer matrix C of size times and a ma trix A defined as A CT C and workout its characteristic equation. Using any software package, determine the eigenvalues and eigenvec tors. Deliverables: The matrices C and A 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 lambda and corre sponding eigenvector x of A Find x x x Compare the values obtained in i with these values. Deliverables: The handwritten code that implements the Power method, the first iterates of eigenvalue generated by the algorithm and the final lambda and x and a comment on the comparison. iii Write a code to construct matrix AAxxTA Use the Power method code written in ii and use it to derive the largest eigenvalue lambda and corresponding eigenvector x of A Find x x x Compare the values obtained in i with these values. Deliverables: The first iterates of lambda and x and a comment on the comparison. iv Write a code to construct matrix AAxxTAxxTA Use the Power method code written in ii and use it to derive the largest eigenvalue lambda and corresponding eigenvector x of A Find x x x Compare the values obtained in i with these values. Deliverables: The first iterates of lambda and x and a comment on the comparison. Dont use any inbuilt python libraries
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