This project computes the two largest eigenvalues of a 50×50 matrix. You will use the usual
Power Method to compute the largest eigenvalue. For the next largest eigenvalue, you can use an
nnihilation or Deflation or Shifting technique$iscussed in class and also in our book. The
matrix A is tridiagonal. Its main diagonal has T on it. The super diagonal (the diagonal above
the main diagonal) has on it. The sub-diagonal (below the main diagonal) has ”. Rest of
the matrix is ¥ro Our starting vector xo has all ones. Our tolerance is 0.01.
Turn in the following on one page
1) Draw Gershgorin Circles that contain the eigenvalues of A.
Mark each radius properly.
2) Based on part (1), what is the spectral radius of A. Print your answer here: _______________
3) With a starting vector xo= [1 1 1 1….1]T, apply the usual power method to estimate ?max , the
dominant- eigenvalue of matrix A. Use a tolerance of 0.01. Print your answer with 4 decimals:
____________
4) Print the number of iterations required to converge. ____________
5) Use the deflation technique discussed in class or in the book, to compute the second largest
eigenvalue. Tolerance = 0.01. Print the second largest eigenvalue with 4 decimals:
_________________
6) Print the number of iterations required for the second largest eigenvalue to converge.
___________
7) Print your computer program here. As discussed in class, the main body of your program is 3
lines, so your
program should not be long.

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