\item Section 6.2: Problems 1(a), 3(a), 5(a) % 26 % 10th ed p383 (all in paper-and-pencil, no programming). \item Section 6.5: Problems 4(a,c), 9(b), 10(b), 12(d), 13. %10th ed p413 Problem 13 is a demonstration of the application of $LU$ decomposition other than solving a linear system. What would be the number of operations (just count multiplications) of straight forward computation of the determinant of an $n\times n$ matrix? In problem 12(d), just count the number of operations to leading order. % find $K$ and $p$ in % the leading order term $K n^p$. In (d), take $m=n$. % % \item \end{enumerate} \end{document} % Remarks: For problem 4 and 9, read Example 3 on page 394 % and the lecture slides from last year's course homepage to find out % how the permutation matrix $P$ can be obtained (and why so). % Next, check out the matlab/octave built-in function 'lu' and see % if your answer is correct. % Review the formula and error bound for finite difference formula. % You will still need them, through the rest of the semester.