2.11. Further Exercises on Linear Algebra

Exercise 2.14

After doing two or all three of Exercise 2.1, Exercise 2.7 and Exercise 2.8 on solving \(A \vec{x} = \vec b\) with

\[\begin{split} A = \left[ \begin{array}{ccc} 4. & 2. & 1. \\ 9. & 3. & 1. \\ 25. & 5. & 1. \end{array} \right], \quad \vec b = \left[ \begin{array}{c} 0.693147 \\ 1.098612 \\ 1.609438 \end{array} \right], \end{split}\]

by three different methods, compare the residuals and the actual errors for the approximate solutions found there.