This project computes the two eigenvalues of a 50x50 matrix. You will use the usual Power...

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This project computes the two eigenvalues of a 50x50 matrix. You will use the usual Power Method to compute the largest eigenvalue. For the other eigenvalue, you will use the Inverse Power Method. Our matrix A is tridiagonal. Its main diagonal has ones on it. The super diagonal (the diagonal above the main diagonal) has negative-ones on it. The sub-diagonal (below the main diagonal) has negative-ones also. Our starting vector x 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. 2) Based on part (1), what is the spectral radius of A. Print your answer here: 3) With a starting vector x.= [1 1 1 1....1], 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: max 4) Print the number of iterations required to converge. 5) Use the Inverse Power Method to compute an eigenvalue closest to 0.8, with tolerance = 0.01 You may use the "inv" command in MATLAB to compute the inverse of a matrix. Print this eigenvalue "closest to 0.88" with 4 decimals: 6) Print the number of iterations required to converge. Do not print your computer program. This project computes the two eigenvalues of a 50x50 matrix. You will use the usual Power Method to compute the largest eigenvalue. For the other eigenvalue, you will use the Inverse Power Method. Our matrix A is tridiagonal. Its main diagonal has ones on it. The super diagonal (the diagonal above the main diagonal) has negative-ones on it. The sub-diagonal (below the main diagonal) has negative-ones also. Our starting vector x 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. 2) Based on part (1), what is the spectral radius of A. Print your answer here: 3) With a starting vector x.= [1 1 1 1....1], 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: max 4) Print the number of iterations required to converge. 5) Use the Inverse Power Method to compute an eigenvalue closest to 0.8, with tolerance = 0.01 You may use the "inv" command in MATLAB to compute the inverse of a matrix. Print this eigenvalue "closest to 0.88" with 4 decimals: 6) Print the number of iterations required to converge. Do not print your computer program.