4.3. (a) Implement inverse iteration with a shift to compute the eigenvalue nearest to 2, and a cor- responding normalized eigenvector, of the matrix [6 2 1 A = 2 3 1 1 1 1 You may use an arbitrary...

Extracted text: 4.3. (a) Implement inverse iteration with a shift to compute the eigenvalue nearest to 2, and a cor- responding normalized eigenvector, of the matrix [6 2 1 A = 2 3 1 1 1 1 You may use an arbitrary starting vector. (b) Use a real symmetric eigensystem library rou- tine to compute all of the eigenvalues and eigen- vectors of the matrix, and compare the results with those obtained in part a.