Reference no: EM13901101
Question 1) Find l∞ and l2 norms of the vectors.
x = (sin k, cos k, 2k)t for a fixed positive integer k
Question 2) Find l∞ norm of the matrices.
Question 3) The following linear system Ax = b have x as the actual solution and x˜ as an approximate solution. Compute ||x-x˜||∞ and ||Ax˜ - b||∞.
a. 1/2x1 + 1/2x2 = 1/63,
1/3x1 + 1/4x2 = 1/168,
x = (1/7 - 1/6)t,
x˜ = (0.142, 0.166)t.
Question 4) Compute the eigenvalues and associated eigenvectors of the following matrices.
Question 5) Find the complex eigenvalues and associated eigenvectors for following matrices.
Question 6) Find the spectral radius for each matrix in question 5.
Question 7) Find the l2 norm for the matrices in question 5.
Question 8) Find the first two iterations of the Jacobi method for the following linear system, using x(0) = 0:
a. 3x1 - x2 + x3 = 1,
3x1 + 6x2 + 2x3 = 0,
3x1 + 3x2 + 7x3 = 4.
Question 9) Give an example of the matrix that is convergent.
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