By using matlab/octave/java,etc

Modify the power method so that it finds the smallest eigenvalue and corresponding eigenvector. You do this by evaluating x(n+1) = A ^-1 x(n )rather than x(n+1 )= Ax(n) When convergence occurs, it is to the eigenvector corresponding to the inverse of the smallest eigenvalue. Demonstrate the validity of your code by running it on a number of test cases