Question

Linear Algebra Project : Dominant Eigenvalue Computation

a. Apply the Power Method to estimate the dominant eigenvalue and a corresponding eigenvector for the matrix A and initial vector x0 below. Stop at k = 5. You can use 5 decimal places maximum if you wish (using rounding). A = 8 0 12 1 −2 1 0 3 0 ; x0 = 1 0 0 (You can also choose any other 3 × 3 or 4 × 4 matrix instead of the matrix and initial vector above, if you wish. Do not use 2 × 2 matrix.)

b. Use the characteristic equation (as seen in class) to nd the exact value of the dominant eigenvalue. Compare with your estimate in part a).

Answer 1