Computer Science, linear Algebra Background

4. Let A be an 'almost tridiagonal, n n matrix whose nonzero pattern is like the nonzero pattern of a tridiagonal matrix except an,10. Here is a 6 6 example: 0000 000 000 00 000 000 In the following, assume that no pivoting is required. (a) What are the nonzero patterns of the matrices L and U of the LU decomposition of A? It is enough to write down the sparsity pattern of the 6 6 example. (b) Suppose now that n is very large. Determine the amount of worlk and storage required for computing the LU decomposition of A. It is sufficient to give your answers in terms of 'big O' notation, and there is no need to provide precise counts. Justify your