Exercises 11.5 Homework
1.
(Theoretical problem.) Find a matrix \(A\) of rank 1 such that
\begin{equation*}
A \begin{pmatrix}
1 \\ 2 \\ 3
\end{pmatrix} = \begin{pmatrix}
3 \\ 1 \\ 5
\end{pmatrix}
\end{equation*}
2.
Use Broyden's method to solve the nonlinear system
\begin{equation*}
\begin{cases}
x^2 + y^2 +\sin(x+y) \amp = a \\
x+y+\cos(xy) \amp = 5
\end{cases}
\end{equation*}
where \(a\) is the number formed by the first two digits of your SUID.
Try at least two different starting points (or more, if needed to find a solution). Report the outcome of running the method for each starting point. Was the root you found always the same?