7.2 (matlab)

90 Chapter 7. Scientific Computing Exercises 7.1, write a function or script that solves the linear system Akx b for a square matrix A and positive integer k, using an LU factorization of A and never explicitly computing the matrix A*. (Hint: Interpret the problem as solving k linear systems sequentially,) 7.2. Suppose A is a full-rank 6 4 matrix. Which of the following is (in exact arithmetic) equal to an identity matrix: AVA or A/A? Why is the other case something other than the identity? 7.3. Examine the eigenvalues of the family of matrices r-2 1 0 011 -2 1 0 0 0 1 -2 1 0 Dy =-N2 0 1 -2 1