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\large{ \bf{ Homework 7 due April 30th,  \\  Numerical Linear Algebra, Spring 2018}}
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\begin{enumerate}
 \item (20pts) Chapter 12, Exercise 10 (implement unpreconditioned CG algorithm from page 339, provide convergence plots). 
 \vskip2ex 
 \item (10pts) Using the Gerschgorin theorem, explain why a strictly diagonally dominant matrix is invertible.
 \vskip2ex
 \item (10pts) Given the matrix
$$A = \begin{pmatrix} 5 & 0.6 & 0.1 \\ -1 & 6 & -0.1 \\ 1 & 0 & 2 \end{pmatrix},$$
find the Gerschgorin row and column disks, and use them to locate the matrix eigenvalues.
 \vskip2ex
 \item (10pts) Chapter 12, Exercise 3.
 \vskip2ex 
 \item (20pts) Chapter 12, Exercise 5, (a) and (b) only. \\
 \textit{Note:} In (a), also determine whether the eigenvalues are real or not.
 In (b), you may use the following stopping criterion for the power iteration: 
 $||A y^{(k)} - \lambda^{(k)} y^{(k)}|| < \text{tol} $. Compare your results with the results of the MATLAB function eig($A$).


\end{enumerate}

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